Truncated great dodecahedral prism

Truncated great dodecahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Tigiddip
Coxeter diagram	x o5/2x5x ()
Elements
Cells	12 pentagrammic prisms, 12 decagonal prisms, 2 truncated great dodecahedra
Faces	30+60 squares, 24 pentagrams, 24 decagons
Edges	60+60+120
Vertices	120
Vertex figure	Sphenoid, edge lengths (√5–1)/2, √5+√5)/2, √(5+√5)/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {19+5{\sqrt {5}}}{8}}}\approx 1.94230$
Hypervolume	$11{\frac {5+3{\sqrt {5}}}{4}}\approx 32.19756$
Dichoral angles	Stip–4–dip: $\arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }$
	Tigid–5/2–stip: 90°
	Tigid–10–dip: 90°
	Dip–4–dip: $\arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }$
Height	1
Central density	3
Number of external pieces	74
Related polytopes
Army	Semi-uniform Tipe
Regiment	Tigiddip
Dual	Small stellapentakis dodecahedral tegum
Conjugate	Quasitruncated small stellated dodecahedral prism
Abstract & topological properties
Euler characteristic	–8
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	No
Nature	Tame

The truncated great dodecahedral prism or tigiddip is a prismatic uniform polychoron that consists of 2 truncated great dodecahedra, 12 pentagrammic prisms, and 12 decagonal prisms. Each vertex joins 1 truncated great dodecahedron, 1 pentagrammic prism, and 2 decagonal prisms. As the name suggests, it is a prism based on the truncated great dodecahedron.

Vertex coordinates

Coordinates for the vertices of a truncated great dodecahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:

• $\left(\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),$
• $\left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {5+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1+{\sqrt {5}}}{2}},\,\pm {\frac {1}{2}}\right).$

External links

• Bowers, Jonathan. "Category 19: Prisms" (#903).

• Klitzing, Richard. "tigiddip".