Elongated triangular gyrobicupola

Elongated triangular gyrobicupola
(3D model) (OFF file)
Rank	3
Type	CRF
Space	Spherical
Notation
Bowers style acronym	Etigybcu
Coxeter diagram	oxxx3xxxo&#xt
Elements
Faces	2+6 triangles, 6+6 squares
Edges	6+6+6+6+12
Vertices	6+12
Vertex figures	6 rectangles, edge lengths 1 and √2
	12 isosceles trapezoids, edge lengths 1, √2, √2, √2
Measures (edge length 1)
Volume	$\frac{10\sqrt2+9\sqrt3}{6} ≈ 4.95510$
Dihedral angles	3–4 join: $\arccos\left(-\frac{2\sqrt2}{3}\right) ≈ 160.52878°$
	4–4 join: $\arccos\left(-\frac{\sqrt6}{3}\right) ≈ 144.73561°$
	3–4 cupolaic: $\arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439°$
	4–4 prismatic: 120°
Central density	1
Related polytopes
Army	Etigybcu
Regiment	Etigybcu
Dual	Gyrodeltodeltoidal octadecahedron
Conjugate	None
Abstract properties
Euler characteristic	2
Topological properties
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	(G2×A1)/2, order 12
Convex	Yes
Nature	Tame

The elongated triangular gyrobicupola is one of the 92 Johnson solids (J₃₆). It consists of 2+6 triangles and 6+6 squares. It can be constructed by inserting a hexagonal prism between the two halves of the cuboctahedron, seen as a triangular gyrobicupola.

Vertex coordinates

An elongated triangular orthobicupola of edge length 1 has the following vertices:

• $\left(±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12\right),$
• $\left(±1,\,0,\,±\frac12\right),$
• $±\left(±\frac12,\,-\frac{\sqrt3}{6},\,\frac{3+2\sqrt3}{6}\right),$
• $±\left(0,\,\frac{\sqrt3}{3},\,\frac{3+2\sqrt3}{6}\right).$

External links

• Klitzing, Richard. "etigybcu".

• Quickfur. "The Elongated Triangular Gyrobicupola".

• Wikipedia Contributors. "Elongated triangular gyrobicupola".
• McCooey, David. "Elongated Triangular Gyrobicupola"