Small dodecicosahedron

Small dodecicosahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Siddy
Elements
Faces	20 hexagons, 12 decagons
Edges	60+60
Vertices	60
Vertex figure	Butterfly, edge lengths √3 and √(5+√5)/2
Measures (edge length 1)
Circumradius	$\sqrt{\frac{17+3\sqrt5}{8}} ≈ 1.72149$
Dihedral angles	6–10 #1: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 79.18768^\circ$
	6–10 #2: $\arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737^\circ$
Central density	even
Number of external pieces	320
Level of complexity	18
Related polytopes
Army	Semi-uniform Srid, edge lengths $\frac{\sqrt5-1}{2}$ (pentagons), 1 (triangles)
Regiment	Siid
Dual	Small dodecicosacron
Conjugate	Great dodecicosahedron
Convex core	Dodecahedron
Abstract & topological properties
Flag count	480
Euler characteristic	–28
Orientable	No
Genus	30
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The small dodecicosahedron, or siddy, is a uniform polyhedron. It consists of 20 hexagons and 12 decagons. Two hexagons and two decagons meet at each vertex..

It is a faceting of the small icosicosidodecahedron, using its 20 hexagons along with the 12 decagons of the small ditrigonal dodecicosidodecahedron.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small icosicosidodecahedron.

External links

• Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#53).

• Klitzing, Richard. "siddy".

• Wikipedia Contributors. "Small dodecicosahedron".
• McCooey, David. "Small Dodecicosahedron"