Augmented hexagonal prism

Augmented hexagonal prism
(3D model) (OFF file)
Rank	3
Type	CRF
Space	Spherical
Notation
Bowers style acronym	Auhip
Coxeter diagram	oxxx oxux&#xt
Elements
Faces	2+2 triangles, 1+2+2 squares, 2 hexagons
Edges	2+2+2+2+2+4+4+4
Vertices	1+4+4+4
Vertex figures	1 square, edge length 1
	4 irregular tetragons, edge lengths 1, 1, √2, √3
	4+4 isosceles triangles, edge lengths (1+√5)/2, √2, √2
Measures (edge length 1)
Volume	$\frac{\sqrt2+9\sqrt3}{6} ≈ 2.83378$
Dihedral angles	3–4: $\arccos\left(-\sqrt{\frac{7+2\sqrt6}{12}}\right) ≈ 174.73561^\circ$
	3–6: $\arccos\left(-\frac{\sqrt6}{3}\right) ≈ 144.73561^\circ$
	4–4: 120°
	3–3: $\arccos\left(-\frac13\right) ≈ 109.47122^\circ$
	4–6: 90°
Central density	1
Related polytopes
Army	Auhip
Regiment	Auhip
Dual	Lateromonotruncated hexagonal tegum
Conjugate	Augmented hexagonal prism
Abstract properties
Euler characteristic	2
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	K2×I, order 4
Convex	Yes
Nature	Tame
Discovered by	{{{discoverer}}}

The augmented hexagonal prism is one of the 92 Johnson solids (J₅₄). It consists of 2+2 triangles, 1+2+2 squares, and 2 hexagons. It can be constructed by attaching a square pyramid to one of the square faces of the hexagonal prism.

Vertex coordinates

An augmented hexagonal prism of edge length 1 has the following vertices:

• $\left(±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12\right),$
• $\left(±1,\,0,\,±\frac12\right),$
• $\left(0,\,\frac{\sqrt2+\sqrt3}{2},\,0\right).$

External links

• Klitzing, Richard. "auhip".

• Quickfur. "The Augmented Hexagonal Prism".

• Wikipedia Contributors. "Augmented hexagonal prism".
• McCooey, David. "Augmented Hexagonal Prism"