Triangular-square duoprism

Triangular-square duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Tisdip
Coxeter diagram	x3o x4o ()
Tapertopic notation	1111
Elements
Cells	4 triangular prisms, 3 cubes
Faces	4 triangles, 3+12 squares
Edges	12+12
Vertices	12
Vertex figure	Digonal disphenoid, edge lengths 1 (base 1) and √2 (base 2 and sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {30}}{6}}\approx 0.91287$
Hypervolume	${\frac {\sqrt {3}}{4}}\approx 0.43301$
Dichoral angles	Trip–4–cube: 90°
	Trip–3–trip: 90°
	Cube–4–cube: 60°
Heights	Square atop cube: ${\frac {\sqrt {3}}{2}}\approx 0.86603$
	Trip atop trip: 1
Central density	1
Number of external pieces	7
Level of complexity	6
Related polytopes
Army	Tisdip
Regiment	Tisdip
Dual	Triangular-square duotegum
Conjugate	None
Abstract & topological properties
Flag count	288
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A2×B2, order 48
Convex	Yes
Nature	Tame

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:

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

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 (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)

External links

• Bowers, Jonathan. "Category A: Duoprisms".

• Klitzing, Richard. "tisdip".

• Quickfur. "The 3,4-Duoprism".

• Wikipedia contributors. "3-4 duoprism".