Small dodecicosidodecahedron

Small dodecicosidodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Saddid
Coxeter diagram	x3/2o5x5*a ()
Elements
Faces	20 triangles, 12 pentagons, 12 decagons
Edges	60+60
Vertices	60
Vertex figure	Crossed isosceles trapezoid, edge lengths 1, √(5+√5)/2, (1+√5)/2, √(5+√5)/2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{11+4\sqrt5}}{2} ≈ 2.23295$
Volume	$2\frac{45+17\sqrt5}{3} ≈ 55.34210$
Dihedral angles	5–10: $\arccos\left(\frac{\sqrt5}{5}\right) ≈ 116.56505^\circ$
	3–10: $\arccos\left(\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 37.37737^\circ$
Central density	2
Number of external pieces	152
Level of complexity	9
Related polytopes
Army	Srid
Regiment	Srid
Dual	Small dodecacronic hexecontahedron
Conjugate	Great dodecicosidodecahedron
Convex core	Dodecahedron
Abstract & topological properties
Flag count	480
Euler characteristic	–16
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The small dodecicosidodecahedron, or saddid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagons, and 12 decagons. One triangle, one pentagon, and two decagons join at each vertex.

It is a faceting of the small rhombicosidodecahedron, using its 12 pentagons and 20 triangles along with 12 additional decagons.

Vertex coordinates

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

Representations

A small dodecicosidodecahedron has the following Coxeter diagrams:

• x3/2o5x5*a
• x5o3ß (, as holosnub)

External links

• Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#40).

• Klitzing, Richard. "saddid".

• Wikipedia Contributors. "Small dodecicosidodecahedron".
• McCooey, David. "Small Dodecicosidodecahedron"