Triangular-hexagonal duoprism

Triangular-hexagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Thiddip
Coxeter diagram	x3o x6o ()
Elements
Cells	6 triangular prisms, 3 hexagonal prisms
Faces	6 triangles, 18 squares, 3 hexagons
Edges	18+18
Vertices	18
Vertex figure	Digonal disphenoid, edge lengths 1 (base 1), √3 (base 2), and √2 (sides)
Measures (edge length 1)
Circumradius	${\frac {2{\sqrt {3}}}{3}}\approx 1.15470$
Hypervolume	${\frac {9}{8}}=1.125$
Dichoral angles	Trip–3–trip: 120°
	Trip–4–hip: 90°
	Hip–6–hip: 60°
Height	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Central density	1
Number of external pieces	9
Level of complexity	6
Related polytopes
Army	Thiddip
Regiment	Thiddip
Dual	Triangular-hexagonal duotegum
Conjugate	None
Abstract & topological properties
Flag count	432
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A2×G2, order 72
Flag orbits	6
Convex	Yes
Nature	Tame

The triangular-hexagonal duoprism or thiddip, also known as the 3-6 duoprism, is a uniform duoprism that consists of 3 hexagonal prisms and 6 triangular prisms, with two of each meeting at each vertex.

The convex hull of two orthogonal triangular-hexagonal duoprisms is either the triangular duoexpandoprism or the triangular duotruncatoprism.

It is also a CRF segmentochoron, being a hexagon atop hexagonal prism. It is designated K-4.47 on Richard Klitzing's list.

Gallery

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  Net

Vertex coordinates

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

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

Representations

A triangular-hexagonal duoprism has the following Coxeter diagrams:

• x3o x6o () (full symmetry)
• x3x x3o () (A₂×A₂ symmetry, hexagon as ditrigon)
• s3s2x3x ()
• ox xx6oo&#x (G₂×A₁ axial, hexagon atop hexagonal prism)
• ox xx3xx&#x (A₂×A₁ axial, as above with ditrigon symmetry)
• xux xxx3ooo&#x (A₂×A₁ axial, triangular prism-first)

External links

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

• Klitzing, Richard. "Thiddip".
• Wikipedia contributors. "3-6 duoprism".