Hexagonal pyramid

The hexagonal pyramid, or hippy, is a pyramid with a hexagonal base and 6 triangles as sides. The version with equilateral triangles as sides is flat, as a regular hexagon can be exactly decomposed into 6 equilateral triangles by a central point. Other variants with isosceles triangles as sides exist as fully valid polyhedra.

It is the vertex-first cap of the triangular tiling, as the arrangement of 6 triangles around a vertex is the same as in that tiling..

Vertex coordinates
A hexagonal pyramid of edge length 1 has the following vertices:


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

These coordinates are a subset of the vertices of the regular triangular tiling.

Representations
A hexagonal pyramid has the following Coxeter diagrams:


 * ox6oo&#x (full symmetry)
 * ox3ox&#x (generally a ditrigonal pyramid)