# Triangular orthobicupola

Triangular orthobicupola Rank3
TypeCRF
SpaceSpherical
Notation
Bowers style acronymTobcu
Coxeter diagramxxx3oxo&#xt
Elements
Faces2+6 triangles, 6 squares
Edges3+3+6+12
Vertices6+6
Vertex figures6 rectangles, edge lengths 1 and 2
6 kites, edge lengths 1 and 2
Measures (edge length 1)
Circumradius$1$ Volume$\frac{5\sqrt2}{3} ≈ 2.35702$ Dihedral angles3–3: $\arccos\left(-\frac79\right) ≈ 141.05756°$ 3–4: $\arccos\left(-\frac{\sqrt3}{3}\right) ≈ 125.26439°$ 4–4: $\arccos\left(-\frac13\right) ≈ 109.47122º$ Central density1
Related polytopes
ArmyTobcu
RegimentTobcu
DualRhombitrapezohedral dodecahedron
ConjugateNone
Abstract & topological properties
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryA2×A1, order 12
ConvexYes
NatureTame

The triangular orthobicupola is one of the 92 Johnson solids (J27). It consists of 2+6 triangles and 6 squares. It can be constructed by attaching two triangular cupolas at their hexagonal bases, such that the two triangular bases are in the same orientation.

If the cupolas are joined such that the bases are rotated 60°, the result is the triangular gyrobicupola, better known as the uniform cuboctahedron. Conversely, a triangular orthobicupola can be thought of as a gyrate cuboctahedron, since it is a cuboctahedron with a cupolaic segment rotated.

The triangular orthobicupola is the vertex figure of the gyrated tetrahedral-octahedral honeycomb.

## Vertex coordinates

A triangular orthobicupola of edge length 1 has vertices given by the following coordinates:

• $\left(±\frac12,\,-\frac{\sqrt3}{6},\,±\frac{\sqrt6}{3}\right),$ • $\left(0,\,\frac{\sqrt3}{3},\,±\frac{\sqrt6}{3}\right),$ • $\left(±\frac12,\,±\frac{\sqrt3}{2},\,0\right),$ • $\left(±1,\,0,\,0\right).$ ## Related polyhedra

A hexagonal prism can be inserted between the two halves of the triangular orthobicupola to produce the elongated triangular orthobicupola.