# Triangular-square duoprism

Triangular-square duoprism Rank4
TypeUniform
SpaceSpherical
Bowers style acronymTisdip
Info
Coxeter diagramx3o x4o
Tapertopic notation1111
SymmetryA2×BC2, order 48
ArmyTisdip
RegimentTisdip
Elements
Vertex figureDigonal disphenoid, edge lengths 1 (base 1) and 2 (base 2 and sides)
Cells4 triangular prisms, 3 cubes
Faces4 triangles, 3+12 squares
Edges12+12
Vertices12
Measures (edge length 1)
Circumradius$\frac{\sqrt{30}}{6} ≈ 0.91287$ Hypervolume$\frac{\sqrt3}{4} ≈ 0.43301$ Dichoral anglesTrip–4–cube: 90°
Trip–3–trip: 90°
Cube–4–cube: 60°
HeightsSquare atop cube: $\frac{\sqrt3}{2} ≈ 0.86603$ Trip atop trip: 1
Central density1
Euler characteristic0
Number of pieces7
Level of complexity6
Related polytopes
DualTriangular-square duotegum
ConjugateTriangular-square duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The triangular-square duoprism or tisdip, also known as the 3-4 duoprism, is a uniform duoprism that consists of 3 cubes and 4 triangular prisms, with two of each meeting at each vertex. It can also be seen as a prism based on the triangular prism, which makes it a convex segmentochoron (designated K-4.18 on Richard Klitzing's) list in two different ways, as a prism of a triangular prism or square atop cube.

## Vertex coordinates

Coordinates for the vertices of a triangular-square duoprism of edge length 1, centered at the origin, are given by:

• $\left(0,\,\frac{\sqrt3}{3},\,±\frac12,\,±\frac12\right),$ • $\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac12,\,±\frac12\right).$ ## Representations

A triangular-square duoprism has the following Coxeter diagrams:

• x3o x4o (full symmetry)
• x x x3o (A2×A1×A1 symmetry, triangular prismatic prism)
• xx xx3oo&#x (A2×A1 axial, prism of triangular prism)
• ox xx4oo&#x (BC2×A1 axial, square atop cube)
• ox xx xx&#x (A1×A1×A1 symmetry, as above with rectangles instead of squares)
• xxx3ooo oqo&#xt (A2×A1 axial, triangle-first)
• xxx xxx&#x (A1×A1 symmetry, 3 squares seen separately)