# Triangular-pentagrammic duoprism

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Triangular-pentagrammic duoprism
Rank4
TypeUniform
Notation
Bowers style acronymTistadip
Coxeter diagramx3o x5/2o ()
Elements
Cells5 triangular prisms, 3 pentagrammic prisms
Faces5 triangles, 15 squares, 3 pentagrams
Edges15+15
Vertices15
Vertex figureDigonal disphenoid, edge lengths 1 (base 1), (5–1)/2 (base 2), 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {25-3{\sqrt {5}}}{30}}}\approx 0.78085}$
Hypervolume${\displaystyle {\frac {\sqrt {75-30{\sqrt {5}}}}{16}}\approx 0.17587}$
Dichoral anglesTrip–4–stip: 90°
Stip–5/2–stip: 60°
Trip–3–trip: 36°
Height${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Central density2
Number of external pieces13
Level of complexity12
Related polytopes
ArmySemi-uniform trapedip
RegimentTistadip
DualTriangular-pentagrammic duotegum
ConjugateTriangular-pentagonal duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryA2×H2, order 60
ConvexNo
NatureTame

The triangular-pentagrammic duoprism or tistadip, also known as the 3-5/2 duoprism, is a uniform duoprism that consists of 3 pentagrammic prisms and 5 triangular prisms, with two of each at each vertex.

## Vertex coordinates

Coordinates for the vertices of a triangular-pentagrammic duoprism with edge length 1 are given by:

• ${\displaystyle \left(0,\,{\frac {\sqrt {3}}{3}},\,0,\,{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right),}$
• ${\displaystyle \left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}}\right),}$
• ${\displaystyle \left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,0,\,{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {{\sqrt {5}}-1}{4}},\,{\sqrt {\frac {5+{\sqrt {5}}}{40}}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {1}{2}},\,-{\sqrt {\frac {5-2{\sqrt {5}}}{20}}}\right),}$