# Elongated triangular gyrobicupola

Elongated triangular gyrobicupola
Rank3
TypeCRF
SpaceSpherical
Notation
Bowers style acronymEtigybcu
Coxeter diagramoxxx3xxxo&#xt
Elements
Faces2+6 triangles, 6+6 squares
Edges6+6+6+6+12
Vertices6+12
Vertex figures6 rectangles, edge lengths 1 and 2
12 isosceles trapezoids, edge lengths 1, 2, 2, 2
Measures (edge length 1)
Volume${\displaystyle \frac{10\sqrt2+9\sqrt3}{6} ≈ 4.95510}$
Dihedral angles3–4 join: ${\displaystyle \arccos\left(-\frac{2\sqrt2}{3}\right) ≈ 160.52878°}$
4–4 join: ${\displaystyle \arccos\left(-\frac{\sqrt6}{3}\right) ≈ 144.73561°}$
3–4 cupolaic: ${\displaystyle \arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439°}$
4–4 prismatic: 120°
Central density1
Related polytopes
ArmyEtigybcu
RegimentEtigybcu
ConjugateNone
Abstract properties
Euler characteristic2
Topological properties
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(G2×A1)/2, order 12
ConvexYes
NatureTame

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:

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