# Truncated great dodecahedral prism

Truncated great dodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymTigiddip
Coxeter diagramx o5/2x5x ()
Elements
Cells12 pentagrammic prisms, 12 decagonal prisms, 2 truncated great dodecahedra
Faces30+60 squares, 24 pentagrams, 24 decagons
Edges60+60+120
Vertices120
Vertex figureSphenoid, edge lengths (5–1)/2, 5+5)/2, (5+5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {19+5{\sqrt {5}}}{8}}}\approx 1.94230}$
Hypervolume${\displaystyle 11{\frac {5+3{\sqrt {5}}}{4}}\approx 32.19756}$
Dichoral anglesStip–4–dip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Tigid–5/2–stip: 90°
Tigid–10–dip: 90°
Dip–4–dip: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
Height1
Central density3
Number of external pieces74
Related polytopes
ArmySemi-uniform Tipe
RegimentTigiddip
DualSmall stellapentakis dodecahedral tegum
ConjugateQuasitruncated small stellated dodecahedral prism
Abstract & topological properties
Euler characteristic–8
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

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:

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