Triangular-octagrammic duoprism

Triangular-octagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Tistodip
Coxeter diagram	x3o x8/3o ()
Elements
Cells	8 triangular prisms, 3 octagrammic prisms
Faces	8 triangles, 24 squares, 3 octagrams
Edges	24+24
Vertices	24
Vertex figure	Digonal disphenoid, edge lengths 1 (base 1), √2–√2(base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {8-3{\sqrt {2}}}{6}}}\approx 0.79134$
Hypervolume	${\frac {{\sqrt {6}}-{\sqrt {3}}}{2}}\approx 0.35872$
Dichoral angles	Trip–4–stop: 90°
	Stop–8/3–stop: 60°
	Trip–3–trip: 45°
Height	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Central density	3
Number of external pieces	19
Level of complexity	12
Related polytopes
Army	Semi-uniform todip, edge lengths 1 (triangle), ${\sqrt {2}}-1$ (octagon)
Regiment	Tistodip
Dual	Triangular-octagrammic duotegum
Conjugate	Triangular-octagonal duoprism
Abstract & topological properties
Flag count	576
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A2×I2(8), order 96
Convex	No
Nature	Tame

The triangular-octagrammic duoprism, also known as tistodip or 3-8/3 duoprism, is a uniform duoprism that consists of 8 triangular prisms and 3 octagrammic prisms, with 2 of each at each vertex.

Vertex coordinates

The coordinates of a triangular-octagrammic duoprism, centered at the origin and with unit edge length, are given by:

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

Representations

A triangular-octagrammic duoprism has the following Coxeter diagrams:

• x3o x8/3o () (full symmetry)
• x3o x4/3x () (A₂×B₂ symmetry, octagrams as ditetragrams)

External links

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

• Klitzing, Richard. "tistodip".