Truncated rhombicosidodecahedron
{{Short description|Type of polyhedron}}
| class="wikitable" bgcolor="#ffffff" cellpadding="5" align="right" style="margin-left:10px" width="240"
!bgcolor=#e7dcc3 colspan=2|Truncated rhombicosidodecahedron | |
| colspan=2 align=center|File:Truncated_small_rhombicosidodecahedron.png | |
| bgcolor=#e7dcc3|Schläfli symbol | trr{5,3} = |
| bgcolor=#e7dcc3|Conway notation | taD = baD |
| bgcolor=#e7dcc3|Faces | 122: 60 {4} 20 {6} 30 {8} 12 {10} |
| bgcolor=#e7dcc3|Edges | 360 |
| bgcolor=#e7dcc3|Vertices | 240 |
| bgcolor=#e7dcc3|Symmetry group | Ih, [5,3], (*532) order 120 |
| bgcolor=#e7dcc3|Rotation group | I, [5,3]+, (532), order 60 |
| bgcolor=#e7dcc3|Dual polyhedron | Disdyakis hexecontahedron 80px |
| bgcolor=#e7dcc3|Properties | convex |
In geometry, the truncated rhombicosidodecahedron is a polyhedron, constructed as a truncated rhombicosidodecahedron. It has 122 faces: 12 decagons, 30 octagons, 20 hexagons, and 60 squares.
Other names
- Truncated small rhombicosidodecahedron
- Beveled icosidodecahedron
Zonohedron
As a zonohedron, it can be constructed with all but 30 octagons as regular polygons. It is 2-uniform, with 2 sets of 120 vertices existing on two distances from its center.
This polyhedron represents the Minkowski sum of a truncated icosidodecahedron, and a rhombic triacontahedron.Eppstein (1996)
Related polyhedra
The truncated icosidodecahedron is similar, with all regular faces, and 4.6.10 vertex figure. Also see the [https://levskaya.github.io/polyhedronisme/?recipe=beD&palette=%23ff0000%20%23ffee00%20%230000ff%20%2300ff00%20%2300ddff%20%23ff00ff truncated rhombirhombicosidodecahedron].
| class=wikitable |
| align=center
!truncated icosidodecahedron !Truncated rhombicosidodecahedron |
| align=center
|160px |160px |
The truncated rhombicosidodecahedron can be seen in sequence of rectification and truncation operations from the icosidodecahedron. A further alternation step leads to the snub rhombicosidodecahedron.
| class=wikitable
!Name !valign=bottom|Icosidodeca- !Truncated rhomb- !Snub rhomb- |
| align=center
!Coxeter !ID (rD) !rID (rrD) !trID (trrD) !srID (htrrD) |
| align=center
!aD !aaD = eD !taaD = baD ![https://levskaya.github.io/polyhedronisme/?recipe=saD&palette=%230000ff%20%23ffee00%20%23ff0000 saD] |
| align=center
!Image |
| align=center
!Conway !jD !oD !maD !gaD |
| align=center
!Dual |
See also
References
{{reflist}}
- {{cite journal
| author = Eppstein, David
| authorlink = David Eppstein
| year = 1996
| title = Zonohedra and zonotopes
| journal = Mathematica in Education and Research
| volume = 5
| issue = 4
| pages = 15–21
| url = http://www.ics.uci.edu/~eppstein/junkyard/ukraine/ukraine.html}}
- Coxeter Regular Polytopes, Third edition, (1973), Dover edition, {{isbn|0-486-61480-8}} (pp. 145–154 Chapter 8: Truncation)
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, {{isbn|978-1-56881-220-5}}
External links
- [http://www.georgehart.com/virtual-polyhedra/conway_notation.html George Hart's Conway interpreter]: generates polyhedra in VRML, taking Conway notation as input
{{Polyhedron-stub}}