Small dodecicosidodecahedron

It shares its vertex arrangement with the small stellated truncated dodecahedron and the uniform compounds of 6 or 12 pentagrammic prisms. It additionally shares its edge arrangement with the rhombicosidodecahedron (having the triangular and pentagonal faces in common), and with the small rhombidodecahedron (having the decagonal faces in common).

{{Uniform polyhedra db|Uniform dual polyhedron stat table|lDID}}

File:Small dodecacronic hexecontahedron.stl

The dual polyhedron to the small dodecicosidodecahedron is the small dodecacronic hexecontahedron (or small sagittal ditriacontahedron). It is visually identical to the small rhombidodecacron. Its faces are darts. A part of each dart lies inside the solid, hence is invisible in solid models.

Faces have two angles of $\backslash arccos(\backslash frac\{5\}\{8\}+\backslash frac\{1\}\{8\}\backslash sqrt\{5\})\backslash approx\; 25.242\backslash ,832\backslash ,961\backslash ,52^\{\backslash circ\}$, one of $\backslash arccos(-\backslash frac\{1\}\{8\}+\backslash frac\{9\}\{40\}\backslash sqrt\{5\})\backslash approx\; 67.783\backslash ,011\backslash ,547\backslash ,44^\{\backslash circ\}$ and one of $360^\{\backslash circ\}-\backslash arccos(-\backslash frac\{1\}\{4\}-\backslash frac\{1\}\{10\}\backslash sqrt\{5\})\backslash approx\; 241.731\backslash ,322\backslash ,529\backslash ,52^\{\backslash circ\}$. Its dihedral angles equal $\backslash arccos(\{\backslash frac\{-19-8\backslash sqrt\{5\}\}\{41\}\})\backslash approx\; 154.121\backslash ,363\backslash ,125\backslash ,78^\{\backslash circ\}$. The ratio between the lengths of the long and short edges is $\backslash frac\{7+\backslash sqrt\{5\}\}\{6\}\backslash approx\; 1.539\backslash ,344\backslash ,662\backslash ,92$.

{{Reflist}}

• {{cite journal| last = Coxeter| first = H. S. M.| authorlink = Harold Scott MacDonald Coxeter| title = Uniform Polyhedra| journal = Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences| volume = 246| issue = 916| date = May 13, 1954| pages = 401–450| doi = 10.1098/rsta.1954.0003| bibcode = 1954RSPTA.246..401C}}
• {{cite book | first=Magnus | last=Wenninger | authorlink=Magnus Wenninger | title=Polyhedron Models | publisher=Cambridge University Press | year=1974 | isbn=0-521-09859-9 | oclc=1738087 }}
• {{Citation | last1=Wenninger | first1=Magnus | author1-link=Magnus Wenninger | title=Dual Models | publisher=Cambridge University Press | isbn=978-0-521-54325-5 |mr=730208 | year=1983}}

• {{MathWorld | urlname=UniformPolyhedron | title=Uniform Polyhedron}}
• {{mathworld | urlname = SmallDodecicosidodecahedron| title = Small dodecicosidodecahedron}}
• {{mathworld|urlname= SmallDodecacronicHexecontahedron|title= Small dodecacronic hexecontahedron}}

Category:Uniform polyhedra

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