Small ditrigonal dodecicosidodecahedron

The small ditrigonal dodecicosidodecahedron, or sidditdid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagrams, and 12 decagons. One triangle, one pentagram, and two decagons join at each vertex.

Small ditrigonal dodecicosidodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sidditdid
Coxeter diagram	x5/3o3x5*a ()
Elements
Faces	20 triangles, 12 pentagrams, 12 decagons
Edges	60+60
Vertices	60
Vertex figure	Crossed isosceles trapezoid, edge lengths 1, √(5+√5)/2, (√5–1)/2, √(5+√5)/2
Measures (edge length 1)
Circumradius	$\sqrt{\frac{17+3\sqrt5}{8}} \approx 1.72149$
Volume	$7\frac{15+\sqrt5}{6} \approx 20.10875$
Dihedral angles	3–10: $\arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) \approx 100.81232^\circ$
	5/2–10: $\arccos\left(\frac{\sqrt5}{4}\right) \approx 63.43495^\circ$
Central density	4
Number of external pieces	212
Level of complexity	13
Related polytopes
Army	Semi-uniform Srid, edge lengths $\frac{\sqrt5-1}{2}$ (pentagons), 1 (triangles)
Regiment	Siid
Dual	Small ditrigonal dodecacronic hexecontahedron
Conjugate	Great ditrigonal dodecicosidodecahedron
Convex core	Dodecahedron
Abstract & topological properties
Flag count	480
Euler characteristic	–16
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

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

Vertex coordinates

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

External links

• Bowers, Jonathan. "Polyhedron Category 4: Trapeziverts" (#52).

• Klitzing, Richard. "sidditdid".

• Wikipedia Contributors. "Small ditrigonal dodecicosidodecahedron".
• McCooey, David. "Small Ditrigonal dodecicosidodecahedron"