Triangular-octagonal duoprism

Triangular-octagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Todip
Coxeter diagram	x3o x8o ()
Elements
Cells	8 triangular prisms, 3 octagonal prisms
Faces	8 triangles, 24 squares, 3 octagons
Edges	24+24
Vertices	24
Vertex figure	Digonal disphenoid, edge lengths 1 (base 1), √2+√2 (base 2), and √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {8+3{\sqrt {2}}}{6}}}\approx 1.42844$
Hypervolume	${\frac {{\sqrt {3}}+{\sqrt {6}}}{2}}\approx 2.09077$
Dichoral angles	Trip–3–trip: 135°
	Trip–4–op: 90°
	Op–8–op: 60°
Height	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Central density	1
Number of external pieces	11
Level of complexity	6
Related polytopes
Army	Todip
Regiment	Todip
Dual	Triangular-octagonal duotegum
Conjugate	Triangular-octagrammic duoprism
Abstract & topological properties
Flag count	576
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A2×I2(8), order 96
Flag orbits	6
Convex	Yes
Nature	Tame

The triangular-octagonal duoprism or todip, also known as the 3-8 duoprism, is a uniform duoprism that consists of 3 octagonal prisms, 8 triangular prisms, with 2 of each meeting at each vertex. It is also a CRF segmentochoron, being octagon atop octagonal prism. It is designated K-4.59 on Richard Klitzing's list.

Gallery

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  Net

Vertex coordinates

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

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

Representations

A triangular-octagonal duoprism has the following Coxeter diagrams:

• x3o x8o () (full symmetry)
• x3o x4x () (A₂×B₂ symmetry, octagon as ditetragon)
• ox xx8oo&#x (octagon atop octagon prism)
• ox xx4xx#&x (B₂×A₁ axial, octagon atop octagon prism)
• xwwx xxxx3oooo&#xt (A₂×A₁ axial, triangular prism-first)

External links

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

• Klitzing, Richard. "todip".
• Wikipedia contributors. "3-8 duoprism".