Triangular cupola

The triangular cupola, or tricu, is one of the 92 Johnson solids. It consists of 1+3 triangles, 3 squares, and 1 hexagon. It is a cupola based on the equilateral triangle.

It can also be constructed as one of the halves formed by cutting a cuboctahedron in half along a hexagonal section.

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


 * (±1/2, –$\sqrt{2}$/6, $\sqrt{2}$/3)
 * (0, $\sqrt{3}$/3, $\sqrt{2}$/3)
 * (±1/2, ±$\sqrt{3}$/2, 0)
 * (0, ±1, 0)

These coordinates can be formed by putting a triangle and hexagon in parallel planes and setting edge lengths to be equal.

Alternatively, it can be formed by removing the vertices of a triangular face from the cuboctahedron, producing the following coordinates:

(±$\sqrt{3}$/2, $\sqrt{3}$/2, 0)
 * (0, ±$\sqrt{6}$/2, $\sqrt{3}$/2)
 * (0, $\sqrt{6}$/2, –$\sqrt{3}$/2)
 * (±$\sqrt{2}$/2, 0 $\sqrt{2}$/2)
 * ($\sqrt{2}$/2, 0, –$\sqrt{2}$/2)
 * ($\sqrt{2}$/2, –$\sqrt{2}$/2, 0)

Related polyhedra
Two triangular cupolas can be attached at their hexagonal bases in the same orientation to form a triangular orthobicupola. If the second cupola is rotated by 60º the result is the triangular gyrobicupola, better known as the cuboctahedron.

A hexagonal prism can be attached to the triangular cupola's hexagonal base to form the elongated triangular cupola. If a hexagonal antiprism is attached instead, the result is the gyroelongated triangular cupola.