# Triangular-square duoprism

Triangular-square duoprism
Rank4
TypeUniform
Notation
Bowers style acronymTisdip
Coxeter diagramx3o x4o ()
Tapertopic notation1111
Elements
Cells4 triangular prisms, 3 cubes
Faces4 triangles, 3+12 squares
Edges12+12
Vertices12
Vertex figureDigonal disphenoid, edge lengths 1 (base 1) and 2 (base 2 and sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {30}}{6}}\approx 0.91287}$
Hypervolume${\displaystyle {\frac {\sqrt {3}}{4}}\approx 0.43301}$
Dichoral anglesTrip–4–cube: 90°
Trip–3–trip: 90°
Cube–4–cube: 60°
HeightsSquare atop cube: ${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Trip atop trip: 1
Central density1
Number of external pieces7
Level of complexity6
Related polytopes
ArmyTisdip
RegimentTisdip
DualTriangular-square duotegum
ConjugateNone
Abstract & topological properties
Flag count288
Euler characteristic0
OrientableYes
Properties
SymmetryA2×B2, order 48
Flag orbits6
ConvexYes
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:

• ${\displaystyle \left(0,\,{\frac {\sqrt {3}}{3}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,-{\frac {\sqrt {3}}{6}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$.

## 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 (B2×A1 axial, square atop cube)
• ox xx xx&#x (K3 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)