# Triangular-pentagrammic duoprism

Triangular-pentagrammic duoprism Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx3o x5/2o
SymmetryA2×H2, order 60
ArmySemi-uniform trapedip
Elements
Vertex figureDigonal disphenoid, edge lengths 1 (base 1), (5–1)/2 (base 2), 2 (sides)
Cells5 triangular prisms, 3 pentagrammic prisms
Faces5 triangles, 15 squares, 3 pentagrams
Edges15+15
Vertices15
Measures (edge length 1)
Circumradius$\sqrt{\frac{25-3\sqrt5}{30}} ≈ 0.78085$ Hypervolume$\frac{\sqrt{75-30\sqrt5}}{16} ≈ 0.17587$ Dichoral anglesTrip–4–stip: 90°
Stip–5/2–stip: 60°
Trip–3–trip: 36°
Height$\frac{\sqrt3}{2} ≈ 0.86603$ Central density2
Euler characteristic0
Number of pieces13
Level of complexity12
Related polytopes
DualTriangular-pentagrammic duotegum
ConjugateTriangular-pentagonal duoprism
Properties
ConvexNo
OrientableYes
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-pentagonal duoprism with edge length 1 are given by:

• $\left(0,\,\frac{\sqrt3}{3},\,0,\,\sqrt{\frac{5-\sqrt5}{10}}\right),$ • $\left(0,\,\frac{\sqrt3}{3},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$ • $\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$ • $\left(±\frac12,\,-\frac{\sqrt3}{6},\,0,\,\sqrt{\frac{5-\sqrt5}{10}}\right),$ • $\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$ • $\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$ 