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User:Tomruen/Uniform operator conversion

Table expanded a bit from [http://ogre.nu/klitzing/explain/polytope-tree.htm], trying to sort out the Bowers naming system.

__TOC__

General (selective)

class=wikitable

! Prefix

! Coxeter-Dynkin diagram
{p,q,r,s,t}

! Bowers adjectives

! Johnson adjectives

align=center bgcolor=#ffffc0

| t0

|{{CDD|node_1|p|node|q|node|r|node|s|node|t|node}}

|colspan=2|regular

align=center bgcolor=#ffffc0

| t1

|{{CDD|node|p|node_1|q|node|r|node|s|node|t|node}}

|colspan=2|rectified

align=center bgcolor=#ffffc0

| t2

|{{CDD|node|p|node|q|node_1|r|node|s|node|t|node}}

|colspan=2|bi-rectified

align=center bgcolor=#ffffc0

| t3

|{{CDD|node|p|node|q|node|r|node_1|s|node|t|node}}

|colspan=2|tri-rectified

align=center bgcolor=#ffffc0

| t4

|{{CDD|node|p|node|q|node|r|node|s|node_1|t|node}}

|colspan=2|quadri-rectified

align=center bgcolor=#ffffc0

| t5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node_1}}

|colspan=2|quinti-rectified

align=center bgcolor=#ffffc0

| t6

|{{CDD|node|p|node|q|node|r|node|s|node|t|node|u|node_1}}

|colspan=2|sexti-rectified

align=center bgcolor=#ffffc0

| t7

|{{CDD|node|p|node|q|node|r|node|s|node|t|node|u|node|v|node_1}}

|colspan=2|septi-rectified

align=center bgcolor=#ffffc0

| t8

|{{CDD|node|p|node|q|node|r|node|s|node|t|node|u|node|v|node|w|node_1}}

|colspan=2|octi-rectified

align=center bgcolor=#ffffc0

| t9

|{{CDD|node|p|node|q|node|r|node|s|node|t|node|u|node|v|node|w|node|x|node_1}}

|colspan=2|noni-rectified

align=center bgcolor=#ffffc0

| t10

|{{CDD|node|p|node|q|node|r|node|s|node|t|node|u|node|v|node|w|node|x|node|y|node_1}}

|colspan=2|deci-rectified

align=center bgcolor=#ffffc0

| t11

|{{CDD|node|p|node|q|node|r|node|s|node|t|node|u|node|v|node|w|node|x|node|y|node|z|node_1}}

|colspan=2|unideci-rectified

align=center bgcolor=#ffc0ff

| t0,1

|{{CDD|node_1|p|node_1|q|node|r|node|s|node|t|node}}

|colspan=2|truncated

align=center bgcolor=#ffc0ff

| t0,2

|{{CDD|node_1|p|node|q|node_1|r|node|s|node|t|node}}

| (small) rhombated

| cantellated / canti-

align=center bgcolor=#ffc0ff

| t0,3

|{{CDD|node_1|p|node|q|node|r|node_1|s|node|t|node}}

| (small) prismated / prismato-

| runcinated / runci-

align=center bgcolor=#ffc0ff

| t0,4

|{{CDD|node_1|p|node|q|node|r|node|s|node_1|t|node}}

| (small) cellated / celli-

| stericated / steri-

align=center bgcolor=#ffc0ff

| t0,5

|{{CDD|node_1|p|node|q|node|r|node|s|node|t|node_1}}

| (small) terated / tera-

| [pentellated / penti-]

align=center bgcolor=#ffc0ff

| t0,6

|{{CDD|node_1|p|node|q|node|r|node|s|node|t|node|u|node_1}}

| (small) petated / peta-

| [hexicated / hexi-]

align=center bgcolor=#ffc0ff

| t0,7

|{{CDD|node_1|p|node|q|node|r|node|s|node|t|node|u|node|v|node_1}}

| (small) exated / exa-

| [heptellated / hepti-]

align=center bgcolor=#ffc0ff

| t0,8

|{{CDD|node_1|p|node|q|node|r|node|s|node|t|node|u|node|v|node|w|node_1}}

| (small) zettated / zetta-

| [octellated / octi-]

align=center bgcolor=#ffc0ff

| t0,9

|{{CDD|node_1|p|node|q|node|r|node|s|node|t|node|u|node|v|node|w|node|x|node_1}}

| (small) yottated / yotta-

| [ennecated / enni-]

align=center

| t1,2

|{{CDD|node|p|node_1|q|node_1|r|node|s|node|t|node}}

|colspan=2|bi-truncated

align=center

| t1,3

|{{CDD|node|p|node_1|q|node|r|node_1|s|node|t|node}}

| (small) bi-rhombated

| bi-cantellated

align=center

| t1,4

|{{CDD|node|p|node_1|q|node|r|node|s|node_1|t|node}}

| (small) bi-prismated

| bi-runcinated

align=center

| t1,5

|{{CDD|node|p|node_1|q|node|r|node|s|node|t|node_1}}

| (small) bi-cellated

| bi-stericated

align=center

| t2,3

|{{CDD|node|p|node|q|node_1|r|node_1|s|node|t|node}}

|colspan=2|tri-truncated

align=center

| t2,4

|{{CDD|node|p|node|q|node_1|r|node|s|node_1|t|node}}

| (small) tri-rhombated

| tri-cantellated

align=center

| t2,5

|{{CDD|node|p|node|q|node_1|r|node|s|node|t|node_1}}

| (small) tri-prismated

| tri-runcinated

align=center

| t3,4

|{{CDD|node|p|node|q|node|r|node_1|s|node_1|t|node}}

|colspan=2|quadri-truncated

align=center

| t3,5

|{{CDD|node|p|node|q|node|r|node_1|s|node|t|node_1}}

| (small) quadri-rhombated

| quadri-cantellated

align=center

| t4,5

|{{CDD|node|p|node|q|node|r|node|s|node_1|t|node_1}}

|colspan=2|quinti-truncated

align=center bgcolor=#ffe0a0

| t0,1,2

|{{CDD|node_1|p|node_1|q|node_1|r|node|s|node|t|node}}

| great rhombated

| cantitruncated

align=center

| t0,1,3

|{{CDD|node_1|p|node_1|q|node|r|node_1|s|node|t|node}}

| prismatotruncated

| runcitruncated

align=center

| t0,1,4

|{{CDD|node_1|p|node_1|q|node|r|node|s|node_1|t|node}}

| cellitruncated

| steritruncated

align=center

| t0,1,5

|{{CDD|node_1|p|node_1|q|node|r|node|s|node|t|node_1}}

| teratruncated

| pentitruncated

align=center

| t0,2,3

|{{CDD|node_1|p|node|q|node_1|r|node_1|s|node|t|node}}

| prismatorhombated

| runcicantellated

align=center

| t0,2,4

|{{CDD|node_1|p|node|q|node_1|r|node|s|node_1|t|node}}

| (small) cellirhombated

| stericantellated

align=center

| t0,2,5

|{{CDD|node_1|p|node|q|node_1|r|node|s|node|t|node_1}}

| (small) terarhombated

| penticantellated

align=center

| t0,3,4

|{{CDD|node_1|p|node|q|node|r|node_1|s|node_1|t|node}}

| celliprismated

| steriruncinated

align=center

| t0,3,5

|{{CDD|node_1|p|node|q|node|r|node_1|s|node|t|node_1}}

| teraprismated

| pentiruncinated

align=center

| t0,4,5

|{{CDD|node_1|p|node|q|node|r|node|s|node_1|t|node_1}}

| teracellated

| pentistericated

align=center

| t1,2,3

|{{CDD|node|p|node_1|q|node_1|r|node_1|s|node|t|node}}

| great bi-rhombated

| bi-cantitruncated

align=center

| t1,2,4

|{{CDD|node|p|node_1|q|node_1|r|node|s|node_1|t|node}}

| bi-prismatotruncated

| bi-runcitruncated

align=center

| t1,2,5

|{{CDD|node|p|node_1|q|node_1|r|node|s|node|t|node_1}}

| bi-cellitruncated

| bi-steritruncated

align=center

| t1,3,4

|{{CDD|node|p|node_1|q|node|r|node_1|s|node_1|t|node}}

| bi-prismatorhombated

| bi-runcicantellated

align=center

| t1,3,5

|{{CDD|node|p|node_1|q|node|r|node_1|s|node|t|node_1}}

| bi-cellirhombated

| bi-stericantellated

align=center

| t1,4,5

|{{CDD|node|p|node_1|q|node|r|node|s|node_1|t|node_1}}

| bi-celliprismated

| bi-steriruncinated

align=center

| t2,3,4

|{{CDD|node|p|node|q|node_1|r|node_1|s|node_1|t|node}}

| great tri-rhombated

| tri-cantitruncated

align=center

| t2,3,5

|{{CDD|node|p|node|q|node_1|r|node_1|s|node|t|node_1}}

| tri-prismatotruncated

| tri-runcitruncated

align=center

| t2,4,5

|{{CDD|node|p|node|q|node_1|r|node|s|node_1|t|node_1}}

| tri-prismatorhombated

| tri-runcicantellated

align=center

| t3,4,5

|{{CDD|node|p|node|q|node|r|node_1|s|node_1|t|node_1}}

| great quadri-rhombated

| quadri-cantitruncated

align=center bgcolor=#ffe0a0

| t0,1,2,3

|{{CDD|node_1|p|node_1|q|node_1|r|node_1|s|node|t|node}}

| great prismated

| runcicantitruncated

align=center

| t0,1,2,4

|{{CDD|node_1|p|node_1|q|node_1|r|node|s|node_1|t|node}}

| great cellirhombated

| stericantitruncated

align=center

| t0,1,2,5

|{{CDD|node_1|p|node_1|q|node_1|r|node|s|node|t|node_1}}

| great terarhombated

| penticantitruncated

align=center

| t0,1,3,4

|...{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| celliprismatotruncated

| steriruncitruncated

align=center

| t0,1,3,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| teraprismatotruncated

| pentiruncitruncated

align=center

| t0,1,4,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| teracellitruncated

| pentisteritruncated

align=center

| t0,2,3,4

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| celliprismatorhombated

| steriruncicantellated

align=center

| t0,2,3,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| teraprismatorhombated

| pentiruncicantellated

align=center

| t0,2,4,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| (small) teracellirhombated

| pentistericantellated

align=center

| t1,2,3,4

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| great bi-prismated

| bi-runcicantitruncated

align=center

| t1,2,3,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| great bi-cellirhombated

| bi-stericantitruncated

align=center

| t1,2,4,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| bi-celliprismatotruncated

| bi-steriruncitruncated

align=center

| t1,3,4,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| bi-celliprismatorhombated

| bi-steriruncicantellated

align=center

| t2,3,4,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| great tri-prismated

| tri-runcicantitruncated

align=center bgcolor=#ffe0a0

| t0,1,2,3,4

|{{CDD|node_1|p|node_1|q|node_1|r|node_1|s|node_1|t|node}}

| great cellated

| steriruncicantitruncated

align=center

| t0,1,2,3,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| great teraprismated

| pentiruncicantitruncated

align=center

| t0,1,2,4,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| great teracellirhombated

| pentistericantitruncated

align=center

| t0,1,3,4,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| teracelliprismatotruncated

| pentisteriruncitruncated

align=center

| t0,2,3,4,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| teracelliprismatorhombated

| pentisteriruncicantellated

align=center

| t1,2,3,4,5

|{{CDD|node|p|node|q|node|r|node|s|node|t|node}}

| great bi-cellated

| bi-steriruncicantitruncated

align=center bgcolor=#ffe0a0

| t0,1,2,3,4,5

|{{CDD|node_1|p|node_1|q|node_1|r|node_1|s|node_1|t|node}}

| great terated

| pentisteriruncicantitruncated

align=center

| t0,last

|{{CDD|node_1|p|node|q|node|r|node|s|node|t|node_1}}

|colspan=2|expanded

align=center bgcolor=#ffe0a0

| tall

|{{CDD|node_1|p|node_1|q|node_1|r|node_1|s|node_1|t|node_1}}

|colspan=2|omnitruncated

5-polytopes

class=wikitable

! Prefix

! Coxeter-Dynkin diagram
{p,q,r,s}

! Bowers adjectives

! Johnson adjectives

align=center bgcolor=#ffffc0

| t0

|{{CDD|node_1|p|node|q|node|r|node|s|node}}

|colspan=2|regular

align=center bgcolor=#ffffc0

| t1

|{{CDD|node|p|node_1|q|node|r|node|s|node}}

|colspan=2|rectified

align=center bgcolor=#ffffc0

| t2

|{{CDD|node|p|node|q|node_1|r|node|s|node}}

|colspan=2|bi-rectified

align=center bgcolor=#ffffc0

| (*) t3

|{{CDD|node|p|node|q|node|r|node_1|s|node}}

|colspan=2|tri-rectified

align=center bgcolor=#ffffc0

| (*) t4

|{{CDD|node|p|node|q|node|r|node|s|node_1}}

|colspan=2|quadri-rectified

align=center bgcolor=#ffc0ff

| t0,1

|{{CDD|node_1|p|node_1|q|node|r|node|s|node}}

|colspan=2|truncated

align=center bgcolor=#ffc0ff

| t0,2

|{{CDD|node_1|p|node|q|node_1|r|node|s|node}}

| (small) rhombated

| cantellated / canti-

align=center bgcolor=#ffc0ff

| t0,3

|{{CDD|node_1|p|node|q|node|r|node_1|s|node}}

| (small) prismated / prismato-

| runcinated / runci-

align=center bgcolor=#ffc0ff

| t0,4

|{{CDD|node_1|p|node|q|node|r|node|s|node_1}}

| (small) cellated / celli-

| stericated / steri-

align=center

| t1,2

|{{CDD|node|p|node_1|q|node_1|r|node|s|node}}

|colspan=2|bi-truncated

align=center

| t1,3

|{{CDD|node|p|node_1|q|node|r|node_1|s|node}}

| (small) bi-rhombated

| bi-cantellated

align=center

| (*) t1,4

|{{CDD|node|p|node_1|q|node|r|node|s|node_1}}

| (small) bi-prismated

| bi-runcinated

align=center

| (*) t2,3

|{{CDD|node|p|node|q|node_1|r|node_1|s|node}}

|colspan=2|tri-truncated

align=center

| (*) t2,4

|{{CDD|node|p|node|q|node_1|r|node|s|node_1}}

| (small) tri-rhombated

| tri-cantellated

align=center

| (*) t3,4

|{{CDD|node|p|node|q|node|r|node_1|s|node_1}}

|colspan=2|quadri-truncated

align=center bgcolor=#ffe0a0

| t0,1,2

|{{CDD|node_1|p|node_1|q|node_1|r|node|s|node}}

| great rhombated

| cantitruncated

align=center

| t0,1,3

|{{CDD|node_1|p|node_1|q|node|r|node_1|s|node}}

| prismatotruncated

| runcitruncated

align=center

| t0,1,4

|{{CDD|node_1|p|node_1|q|node|r|node|s|node_1}}

| cellitruncated

| steritruncated

align=center

| t0,2,3

|{{CDD|node_1|p|node|q|node_1|r|node_1|s|node}}

| prismatorhombated

| runcicantellated

align=center

| t0,2,4

|{{CDD|node_1|p|node|q|node_1|r|node|s|node_1}}

| (small) cellirhombated

| stericantellated

align=center

| (*) t0,3,4

|{{CDD|node_1|p|node|q|node|r|node_1|s|node_1}}

| celliprismated

| steriruncinated

align=center

| t1,2,3

|{{CDD|node|p|node_1|q|node_1|r|node_1|s|node}}

| great bi-rhombated

| bi-cantitruncated

align=center

| (*) t1,2,4

|{{CDD|node|p|node_1|q|node_1|r|node|s|node_1}}

| bi-prismatotruncated

| bi-runcitruncated

align=center

| (*) t1,3,4

|{{CDD|node|p|node_1|q|node|r|node_1|s|node_1}}

| bi-prismatorhombated

| bi-runcicantellated

align=center

| (*) t2,3,4

|{{CDD|node|p|node|q|node_1|r|node_1|s|node_1}}

| great tri-rhombated

| tri-cantitruncated

align=center bgcolor=#ffe0a0

| t0,1,2,3

|{{CDD|node_1|p|node_1|q|node_1|r|node_1|s|node}}

| great prismated

| runcicantitruncated

align=center

| t0,1,2,4

|{{CDD|node_1|p|node_1|q|node_1|r|node|s|node_1}}

| great cellirhombated

| stericantitruncated

align=center

| (*) t0,1,3,4

| {{CDD|node_1|p|node_1|q|node|r|node_1|s|node_1}}

| celliprismatotruncated

| steriruncitruncated

align=center

| (*) t0,2,3,4

|{{CDD|node_1|p|node|q|node_1|r|node_1|s|node_1}}

| celliprismatorhombated

| steriruncicantellated

align=center

| (*) t1,2,3,4

|{{CDD|node|p|node_1|q|node_1|r|node_1|s|node_1}}

| great bi-prismated

| bi-runcicantitruncated

align=center bgcolor=#ffe0a0

| t0,1,2,3,4

|{{CDD|node_1|p|node_1|q|node_1|r|node_1|s|node_1}}

| great cellated

| steriruncicantitruncated

align=center bgcolor=#ffe0a0

| tall

|{{CDD|node_1|p|node_1|q|node_1|r|node_1|s|node_1}}

|colspan=2|omnitruncated

4-polytopes

class=wikitable

! Prefix

! Coxeter-Dynkin diagram
{p,q,r}

! Bowers adjectives

! Johnson adjectives

align=center bgcolor=#ffffc0

| t0

|{{CDD|node_1|p|node|q|node|r|node}}

|colspan=2|regular

align=center bgcolor=#ffffc0

| t1

|{{CDD|node|p|node_1|q|node|r|node}}

|colspan=2|rectified

align=center bgcolor=#ffffc0

| (*) t2

|{{CDD|node|p|node|q|node_1|r|node}}

|colspan=2|bi-rectified

align=center bgcolor=#ffffc0

| (*) t3

|{{CDD|node|p|node|q|node|r|node_1}}

|colspan=2|tri-rectified

align=center bgcolor=#ffc0ff

| t0,1

|{{CDD|node_1|p|node_1|q|node|r|node}}

|colspan=2|truncated

align=center bgcolor=#ffc0ff

| t0,2

|{{CDD|node_1|p|node|q|node_1|r|node}}

| (small) rhombated

| cantellated / canti-

align=center bgcolor=#ffc0ff

| t0,3

|{{CDD|node_1|p|node|q|node|r|node_1}}

| (small) prismated / prismato-

| runcinated / runci-

align=center

| t1,2

|{{CDD|node|p|node_1|q|node_1|r|node}}

|colspan=2|bi-truncated

align=center

| (*) t1,3

|{{CDD|node|p|node_1|q|node|r|node_1}}

| (small) bi-rhombated

| bi-cantellated

align=center

| (*) t2,3

|{{CDD|node|p|node|q|node_1|r|node_1}}

|colspan=2|tri-truncated

align=center bgcolor=#ffe0a0

| t0,1,2

|{{CDD|node_1|p|node_1|q|node_1|r|node}}

| great rhombated

| cantitruncated

align=center

| t0,1,3

|{{CDD|node_1|p|node_1|q|node|r|node_1}}

| prismatotruncated

| runcitruncated

align=center

| (*) t0,2,3

|{{CDD|node_1|p|node|q|node_1|r|node_1}}

| prismatorhombated

| runcicantellated

align=center

| (*) t1,2,3

|{{CDD|node|p|node_1|q|node_1|r|node_1}}

| great bi-rhombated

| bi-cantitruncated

align=center bgcolor=#ffe0a0

| t0,1,2,3

|{{CDD|node_1|p|node_1|q|node_1|r|node_1}}

| great prismated

| runcicantitruncated

align=center bgcolor=#ffe0a0

| tall

|{{CDD|node_1|p|node_1|q|node_1|r|node_1}}

|colspan=2|omnitruncated

3-polytopes

class=wikitable

! Prefix

! Coxeter-Dynkin diagram
{p,q}

! Bowers adjectives

! Johnson adjectives

align=center bgcolor=#ffffc0

| t0

|{{CDD|node_1|p|node|q|node}}

|colspan=2|regular

align=center bgcolor=#ffffc0

| t1

|{{CDD|node|p|node_1|q|node}}

|colspan=2|rectified

align=center bgcolor=#ffffc0

| (*) t2

|{{CDD|node|p|node|q|node_1}}

|colspan=2|bi-rectified

align=center bgcolor=#ffc0ff

| t0,1

|{{CDD|node_1|p|node_1|q|node}}

|colspan=2|truncated

align=center bgcolor=#ffc0ff

| t0,2

|{{CDD|node_1|p|node|q|node_1}}

| (small) rhombated

| cantellated / canti-

align=center

| (*) t1,2

|{{CDD|node|p|node_1|q|node_1}}

|colspan=2|bi-truncated

align=center bgcolor=#ffe0a0

| t0,1,2

|{{CDD|node_1|p|node_1|q|node_1}}

| great rhombated

| cantitruncated

align=center bgcolor=#ffe0a0

| tall

|{{CDD|node_1|p|node_1|q|node_1}}

|colspan=2|omnitruncated

2-polytopes

class=wikitable

! Prefix

! Coxeter-Dynkin diagram
{p}

! Bowers adjectives

! Johnson adjectives

align=center bgcolor=#ffffc0

| t0

|{{CDD|node_1|p|node}}

|colspan=2|regular

align=center bgcolor=#ffffc0

| (*) t1

|{{CDD|node|p|node_1}}

|colspan=2|rectified

align=center bgcolor=#ffc0ff

| t0,1

|{{CDD|node_1|p|node_1}}

|colspan=2|truncated

align=center bgcolor=#ffe0a0

| tall

|{{CDD|node_1|p|node_1}}

|colspan=2|omnitruncated

(*) unneeded - can be made by reverse construction

4-polytopes explicit

class=wikitable
align=center

! Prefix

|t0

|t1

|t2

|t3

|t0,1

|t0,2

|t0,3

|t1,2

|t1,3

|t2,3

|t0,1,2

|t0,1,3

|t0,2,3

|t1,2,3

|t0,1,2,3

align=center

! Coxeter-Dynkin diagram
{p,q,r}

|{{CDD|node_1|p|node|q|node|r|node}}

|{{CDD|node|p|node_1|q|node|r|node}}

|{{CDD|node|p|node|q|node_1|r|node}}

|{{CDD|node|p|node|q|node|r|node_1}}

|{{CDD|node_1|p|node_1|q|node|r|node}}

|{{CDD|node_1|p|node|q|node_1|r|node}}

|{{CDD|node_1|p|node|q|node|r|node_1}}

|{{CDD|node|p|node_1|q|node_1|r|node}}

|{{CDD|node|p|node_1|q|node|r|node_1}}

|{{CDD|node|p|node|q|node_1|r|node_1}}

|{{CDD|node_1|p|node_1|q|node_1|r|node}}

|{{CDD|node_1|p|node_1|q|node|r|node_1}}

|{{CDD|node_1|p|node|q|node_1|r|node_1}}

|{{CDD|node|p|node_1|q|node_1|r|node_1}}

|{{CDD|node_1|p|node_1|q|node_1|r|node_1}}

align=center

!Johnson prefix

!regular

!rectified

!bi-rectified

!tri-rectified

!truncated

|cantellated

|runcinated

|bi-truncated

|bi-cantellated

|tri-truncated

|cantitruncated

|runcitruncated

|runcicantellated

|bi-cantitruncated

|runcicantitruncated
(omnitruncated)

align=center

!Bowers prefix

!regular

!rectified

!bi-rectified

!tri-rectified

!truncated

|rhombated

|prismated

|bi-truncated

|bi-rhombated

|tri-truncated

|great rhombated

|prismatotruncated

|prismatorhombated

|great bi-rhombated

|great prismated

align=center

!{3,3,3}

|{{CDD|node_1|3|node|3|node|3|node}}

|{{CDD|node|3|node_1|3|node|3|node}}

|{{CDD|node|3|node|3|node_1|3|node}}

|{{CDD|node|3|node|3|node|3|node_1}}

|{{CDD|node_1|3|node_1|3|node|3|node}}

|{{CDD|node_1|3|node|3|node_1|3|node}}

|{{CDD|node_1|3|node|3|node|3|node_1}}

|{{CDD|node|3|node_1|3|node_1|3|node}}

|{{CDD|node|3|node_1|3|node|3|node_1}}

|{{CDD|node|3|node|3|node_1|3|node_1}}

|{{CDD|node_1|3|node_1|3|node_1|3|node}}

|{{CDD|node_1|3|node_1|3|node|3|node_1}}

|{{CDD|node_1|3|node|3|node_1|3|node_1}}

|{{CDD|node|3|node_1|3|node_1|3|node_1}}

|{{CDD|node_1|3|node_1|3|node_1|3|node_1}}

align=center

!Johnson

!5-cell

!rectified 5-cell

!bi-rectified 5-cell

!tri-rectified 5-cell

!truncated 5-cell

|cantellated 5-cell

|runcinated 5-cell

|bi-truncated 5-cell

|bi-cantellated 5-cell

|tri-truncated 5-cell

|cantitruncated 5-cell

|runcitruncated 5-cell

|runcicantellated 5-cell

|bi-cantitruncated 5-cell

|omnitruncated 5-cell

align=center

!Bowers

!pentachoron
(pen)

!rectified pentachoron
(rap)

!bi-rectified pentachoron

!tri-rectified pentachoron

!truncated pentachoron
(tip)

|rhombated pentachoron
(srip)

|prismodecachoron
(spid)

|decachoron
(deca)

|bi-rhombated pentachoron

|tri-truncated pentachoron

|great rhombated pentachoron
(grip)

|prismatotruncated pentachoron

|prismatorhombated pentachoron
(prip)

|great bi-rhombated pentachoron

|great prismatodecachoron
(gippid)

align=center

!{4,3,3}

|{{CDD|node_1|4|node|3|node|3|node}}

|{{CDD|node|4|node_1|3|node|3|node}}

|{{CDD|node|4|node|3|node_1|3|node}}

|{{CDD|node|4|node|3|node|3|node_1}}

|{{CDD|node_1|4|node_1|3|node|3|node}}

|{{CDD|node_1|4|node|3|node_1|3|node}}

|{{CDD|node_1|4|node|3|node|3|node_1}}

|{{CDD|node|4|node_1|3|node_1|3|node}}

|{{CDD|node|4|node_1|3|node|3|node_1}}

|{{CDD|node|4|node|3|node_1|3|node_1}}

|{{CDD|node_1|4|node_1|3|node_1|3|node}}

|{{CDD|node_1|4|node_1|3|node|3|node_1}}

|{{CDD|node_1|4|node|3|node_1|3|node_1}}

|{{CDD|node|4|node_1|3|node_1|3|node_1}}

|{{CDD|node_1|4|node_1|3|node_1|3|node_1}}

align=center

!Johnson

!8-cell

!rectified 8-cell

!bi-rectified 8-cell

!tri-rectified 8-cell

!truncated 8-cell

|cantellated 8-cell

|runcinated 8-cell

|bi-truncated 8-cell

|bi-cantellated 8-cell

|tri-truncated 8-cell

|cantitruncated 8-cell

|runcitruncated 8-cell

|runcicantellated 8-cell

|bi-cantitruncated 8-cell

|omnitruncated 8-cell

align=center

!Bowers prefix

!tesseract
(tes)

!rectified tesseract
(rit)

!bi-rectified tesseract

rectified hexadecachoron
[24-cell]

!tri-rectified tesseract

hexadecachoron
(hex)

!truncated tesseract
(tat)

|rhombated tesseract
(srit)

|prismatotesseractihexadecachoron
(sidpith)

|tesseractihexadecachoron
(tah)

|bi-rhombated tesseract

rhombated hexadecachoron
[r.24-cell]

|tri-truncated tesseract

truncated hexadecachoron
(thex)

|great rhombated tesseract
(grit)

|prismatotruncated tesseract

prismatorhombated hexadecachoron
(proh)

|prismatorhombated tesseract
(prit)

|great bi-rhombated tesseract

great rhombated hexadecachoron
[tr.24-cell]

|great prismatotesseractihexadecachoron
(gidpith)

align=center

!{3,4,3}

|{{CDD|node_1|3|node|4|node|3|node}}

|{{CDD|node|3|node_1|4|node|3|node}}

|{{CDD|node|3|node|4|node_1|3|node}}

|{{CDD|node|3|node|4|node|3|node_1}}

|{{CDD|node_1|3|node_1|4|node|3|node}}

|{{CDD|node_1|3|node|4|node_1|3|node}}

|{{CDD|node_1|3|node|4|node|3|node_1}}

|{{CDD|node|3|node_1|4|node_1|3|node}}

|{{CDD|node|3|node_1|4|node|3|node_1}}

|{{CDD|node|3|node|4|node_1|3|node_1}}

|{{CDD|node_1|3|node_1|4|node_1|3|node}}

|{{CDD|node_1|3|node_1|4|node|3|node_1}}

|{{CDD|node_1|3|node|4|node_1|3|node_1}}

|{{CDD|node|3|node_1|4|node_1|3|node_1}}

|{{CDD|node_1|3|node_1|4|node_1|3|node_1}}

align=center

!Johnson

!24-cell

!rectified 24-cell

!bi-rectified 24-cell

!tri-rectified 24-cell

!truncated 24-cell

|cantellated 24-cell

|runcinated 24-cell

|bi-truncated 24-cell

|bi-cantellated 24-cell

|tri-truncated 24-cell

|cantitruncated 24-cell

|runcitruncated 24-cell

|runcicantellated 24-cell

|bi-cantitruncated 24-cell

|omnitruncated 24-cell

align=center

!Bowers

!icositetrachoron
(ico)

!rectified icositetrachoron
(rico)

!bi-rectified icositetrachoron

!tri-rectified icositetrachoron

!truncated icositetrachoron
(tico)

|rhombated icositetrachoron
(srico)

|prismotetracontaoctachoron
(spic)

|tetracontaoctachoron
(cont)

|bi-rhombated icositetrachoron

|tri-truncated icositetrachoron

|great rhombated icositetrachoron
(grico)

|prismatotruncated icositetrachoron

|prismatorhombated icositetrachoron
(prico)

|great bi-rhombated icositetrachoron

|great prismatotetracontaoctachoron
(gippic)

align=center

!{5,3,3}

|{{CDD|node_1|5|node|3|node|3|node}}

|{{CDD|node|5|node_1|3|node|3|node}}

|{{CDD|node|5|node|3|node_1|3|node}}

|{{CDD|node|5|node|3|node|3|node_1}}

|{{CDD|node_1|5|node_1|3|node|3|node}}

|{{CDD|node_1|5|node|3|node_1|3|node}}

|{{CDD|node_1|5|node|3|node|3|node_1}}

|{{CDD|node|5|node_1|3|node_1|3|node}}

|{{CDD|node|5|node_1|3|node|3|node_1}}

|{{CDD|node|5|node|3|node_1|3|node_1}}

|{{CDD|node_1|5|node_1|3|node_1|3|node}}

|{{CDD|node_1|5|node_1|3|node|3|node_1}}

|{{CDD|node_1|5|node|3|node_1|3|node_1}}

|{{CDD|node|5|node_1|3|node_1|3|node_1}}

|{{CDD|node_1|5|node_1|3|node_1|3|node_1}}

align=center

!Johnson

!120-cell

!rectified 120-cell

!bi-rectified 120-cell

!tri-rectified 120-cell

!truncated 120-cell

|cantellated 120-cell

|runcinated 120-cell

|bi-truncated 120-cell

|bi-cantellated 120-cell

|tri-truncated 120-cell

|cantitruncated 120-cell

|runcitruncated 120-cell

|runcicantellated 120-cell

|bi-cantitruncated 120-cell

|omnitruncated 120-cell

align=center

!Bowers prefix

!hecatonicosachoron
(hi)

!rectified hecatonicosachoron
(rahi)

!bi-rectified hecatonicosachoron

rectified hecatonicosachoron
(rox)

!tri-rectified hecatonicosachoron

hexacosichoron
(ex)

!truncated hecatonicosachoron
(thi)

|rhombated hecatonicosachoron
(srahi)

|prismatohexacosihecatonicosachoron
(sidpixhi)

|hexacosihecatonicosachoron
(xhi)

|bi-rhombated hecatonicosachoron
rhombated hexacosichoron
(srix)

|tri-truncated hecatonicosachoron

truncated hexacosichoron
(tex)

|great rhombated hecatonicosachoron
(grahi)

|prismatotruncated hecatonicosachoron

prismatorhombated hexacosichoron
(prix)

|prismatorhombated hecatonicosachoron
(prahi)

|great bi-rhombated hecatonicosachoron

great rhombated hexacosichoron
(grix)

|great prismatohexacosihecatonicosachoron
(gidpixhi)

Johnson



http://www.mathconsult.ch/lists/cgi/private/polyhedron/2006b/msg00273.html Higher Wythoffian operators (Johnson)


    

  • 



a.. From: "Norman Johnson"


b.. Subject: Re: [Polyhedron] Higher Wythoffian operators


c.. Date: Mon, 31 Jul 2006 12:25:03 -0400


d.. To: "Polyhedron Discussion List" 


My names for the operations corresponding to ringing various


nodes of a Coxeter diagram for a reflection group, thereby converting


it into a Wythoff diagram for a uniform polytope or honeycomb, are


as follows:


t_0  original


t_1  rectified


t_2  birectified


t_3  trirectified


t_4  quadrirectified


t_5  quintirectified


. . .


t_0,1  truncated


t_1,2  bitruncated


t_2,3  tritruncated


. . .


t_0,2  cantellated


t_1,3  bicantellated


t_2,4  tricantellated


. . .


t_0,3  runcinated


t_1,4  biruncinated


t_2,5  triruncinated


. . .


t_0,4  stericated


t_1,5  bistericated


t_2,6  tristericated


. . .


t_0,1,2  cantitruncated


t_1,2,3  bicantitruncated


t_2,3,4  tricantitruncated


. . .


t_0,1,3  runcitruncated


t_1,2,4  biruncitruncated


t_2,3,5  triruncitruncated


. . .


t_0,1,4  steritruncated


t_1,2,5  bisteritruncated


t_2,3,6  tristeritruncated


. . .


t_0,2,3  runcicantellated


t_1,3,4  biruncicantellated


t_2,4,5  triruncicantellated


. . .


t_0,1,2,3  runcicantitruncated


t_1,2,3,4  biruncicantitruncated


t_2,3,4,5  triruncicantitruncated


If only the end nodes 0 and n are ringed, the term "expanded" can


be used; when all nodes are ringed, the term is "omnitruncated."


It should be borne in mind that these operations apply to regular


figures and others whose Wythoff diagrams have their nodes numbered


from left to right.


I have not invented TOCID equivalents for n-polytopes or (n-1)-


honeycombs with n > 4.


Norman

Bowers



http://www.mathconsult.ch/lists/cgi/private/polyhedron/2006b/msg00270.html


    

  • 



Subject: Re: [Polyhedron] Higher Wythoffian operators? nth order rectification and truncation?


Date: Mon, 31 Jul 2006 17:48:11 +0200


Cc: polyhedron@lists.mathconsult.ch


Tom asked for a rule based naming according to Wythoff's kaleidoscopical


construction, i.e. a naming scheme which translates the decoration of Dynkin


diagrams into names. This was given twice within the archive. One by


Jonathan Bowers, one by Norman Johnson (the ndiffering names in parantheses).


In what follows this system is given with respect to 6-dimensional linear


Dynkin diagrams. Obviously, the higher the dimension, the more additional


operators will be needed. [+pentellated/penti]


000001 - regular


000010 - rectated


000011 - truncated


000100 - birectated


000101 - small rhombated (cantellated)


000110 - bitruncated


000111 - great rhombated (cantitruncated)


001001 - small prismated (runcinated)


001010 - small birhombated (bicantellated)


001011 - prismatotruncated (runcitruncated)


001100 - tritruncated


001101 - prismatorhombated (runcicantellated)


001110 - great birhombated (bicantitruncated)


001111 - great prismated (runcicantitruncated)


010001 - small cellated (stericated)


010010 - small biprismated (biruncinated)


010011 - cellitruncated (steritruncated)


010101 - small cellirhombated (stericantellated)


011010 - biprismatorhombated (biruncitruncated)


010111 - great cellirhombated (stericantitruncated)


011001 - celliprismated (steriruncinated)


011011 - celliprismatotruncated (steriruncitruncated)


011101 - celliprismatorhombated (steriruncicantellated)


011110 - great biprismated (biruncicantitruncated)


011111 - great cellated (steriruncicantitruncated)


100001 - small terated [pentellated]


110001 - teracellated [pentitruncated]


101001 - small teraprismated [penticantellated]


111001 - teracelliprismated [penticantitruncated]


110101 - small teracellirhombated [pentiruncitruncated]


101101 - teraprismatorhombated [pentiruncicantellated]


101111 - great teraprismated [pentiruncicantitruncated]


110011 - teracellitruncated [pentisteritruncated]


110111 - great teracellirhombated (pentistericantitruncated]


111111 - great terated [pentisteriruncicantitruncated = omnitruncated]