Hexagonal pyramid
# Hexagonal pyramid

In geometry, a hexagonal pyramid or hexacone is a pyramid with a hexagonal base upon which are erected six isosceles triangular faces that meet at a point (the apex). Like any pyramid, it is self-dual.

A right hexagonal pyramid with a regular hexagon base has $C_{6v}$ symmetry.

A right regular pyramid is one which has a regular polygon as its base and whose apex is "above" the center of the base, so that the apex, the center of the base and any other vertex form a right triangle.

## Vertex coordinates

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

* $\left(\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,0\right)$
* $\left(\pm 1,\,0,\,0\right)$
* $\left(0,\,0,\,0\right)$

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)

## Related polyhedra

Regular pyramids :

| Digonal | Triangular | Square | Pentagonal | Hexagonal | Heptagonal | Octagonal | Enneagonal | Decagonal... |
| - | - | - | - | - | - | - | - | - |
| Improper | Regular | Equilateral | Equilateral | Isosceles | Isosceles | Isosceles | Isosceles | Isosceles |
