Small ditrigonary icosidodecahedral prism

Small ditrigonary icosidodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sidtiddip
Coxeter diagram	x x5/2o3o3*b ()
Elements
Cells	20 triangular prisms, 12 pentagrammic prisms, 2 small ditrigonary icosidodecahedra
Faces	40 triangles, 60 squares, 24 pentagrams
Edges	20+120
Vertices	40
Vertex figure	ditrigonal pyramid, edge lengths 1, (√5–1)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	1
Hypervolume	${\frac {4{\sqrt {5}}}{3}}\approx 2.98142$
Dichoral angles	Trip–4–stip: $\arccos \left(-{\sqrt {\frac {5+2{\sqrt {5}}}{15}}}\right)\approx 142.62263^{\circ }$
	Sidtid–3–trip: 90°
	Sidtid–5/2–stip: 90°
Height	1
Central density	2
Number of external pieces	74
Related polytopes
Army	Semi-uniform Dope
Regiment	Sidtiddip
Dual	Small triambic icosahedral tegum
Conjugate	Great ditrigonary icosidodecahedral prism
Abstract & topological properties
Euler characteristic	–10
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The small ditrigonary icosidodecahedral prism or sidtiddip, is a prismatic uniform polychoron that consists of 2 small ditrigonary icosidodecahedra, 12 pentagrammic prisms, and 20 triangular prisms. Each vertex joins 1 small ditrigonary icosidodecahedron, 3 pentagrammic prisms, and 3 triangular prisms. As the name suggests, it is a prism based on the small ditrigonary icosidodecahedron.

The small ditrigonary icosidodecahedral prism can be vertex-inscribed into the small stellated hecatonicosachoron.

Vertex coordinates

The vertices of a small ditrigonary icosidodecahedral prism of edge length 1 are given by all permutations and changes of sign of the first three coordinates of:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),$

along with all even permutations and all sign changes of:

• $\left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,0,\,\pm {\frac {1}{2}}\right).$

The first set of vertices are those of an inscribed tesseract, seen as a cubic prism.

External links

• Bowers, Jonathan. "Category 19: Prisms" (#920).

• Klitzing, Richard. "sidtiddip".