# Decagonal-snub cubic duoprism

Decagonal-snub cubic duoprism
Rank5
TypeUniform
Notation
Bowers style acronymDasnic
Coxeter diagramx10o s4s3s ()
Elements
Tera8+24 triangular-decagonal duoprisms, 6 square-decagonal duoprisms, 10 snub cubic prisms
Cells80+240 triangular prisms, 60 cubes, 12+24+24 decagonal prisms, 10 snub cubes
Faces80+240 triangles, 60+120+240+240 squares, 24 decagons
Edges120+240+240+240
Vertices240
Vertex figureMirror-symmetric pentagonal scalene, edge lengths 1, 1, 1, 1, 2 (base pentagon), (5+5)/2 (top edge), 2 (side edges)
Measures (edge length 1)
Hypervolume≈ 60.70331
Sniccup–snic–sniccup: 144°
Central density1
Number of external pieces48
Level of complexity50
Related polytopes
ArmyDasnic
RegimentDasnic
DualDecagonal-pentagonal icositetrahedral duotegum
ConjugateDecagrammic-snub cubic duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryB3+×I2(10), order 480
ConvexYes
NatureTame

The decagonal-snub cubic duoprism or dasnic is a convex uniform duoprism that consists of 10 snub cubic prisms, 6 square-decagonal duoprisms, and 32 triangular-decagonal duoprisms of two kinds. Each vertex joins 2 snub cubic prisms, 4 triangular-decagonal duoprisms, and 1 square-decagonal duoprism.

## Vertex coordinates

The vertices of a decagonal-snub cubic duoprism of edge length 1 are given by by all even permutations with an even number of sign changes, plus all odd permutations with an odd amount of sign changes, of the last three coordinates of:

• ${\displaystyle \left(0,\,\pm {\frac {1+{\sqrt {5}}}{2}},\,c_{1},\,c_{2},\,c_{3}\right),}$
• ${\displaystyle \left(\pm {\sqrt {\frac {5+{\sqrt {5}}}{8}}},\,\pm {\frac {3+{\sqrt {5}}}{4}},\,c_{1},\,c_{2},\,c_{3}\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {5+2{\sqrt {5}}}}{2}},\,\pm {\frac {1}{2}},\,c_{1},\,c_{2},\,c_{3}\right),}$

where

• ${\displaystyle c_{1}={\sqrt {{\frac {1}{12}}\left(4-{\sqrt[{3}]{17+3{\sqrt {33}}}}-{\sqrt[{3}]{17-3{\sqrt {33}}}}\right)}},}$
• ${\displaystyle c_{2}={\sqrt {{\frac {1}{12}}\left(2+{\sqrt[{3}]{17+3{\sqrt {33}}}}+{\sqrt[{3}]{17-3{\sqrt {33}}}}\right)}},}$
• ${\displaystyle c_{3}={\sqrt {{\frac {1}{12}}\left(4+{\sqrt[{3}]{199+3{\sqrt {33}}}}+{\sqrt[{3}]{199-3{\sqrt {33}}}}\right)}}.}$