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Hexagonal pyramid

## Summary

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.

Hexagonal pyramid
TypePyramid
Faces6 triangles
1 hexagon
Edges12
Vertices7
Vertex configuration6(32.6)
(36)
Schläfli symbol( ) ∨ {6}
Symmetry groupC6v, [6], (*66)
Rotation groupC6, [6]+, (66)
Dual polyhedronSelf-dual
PropertiesConvex
Net

A right hexagonal pyramid with a regular hexagon base has C6v 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:

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

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

## Representations

STL Hexagonal pyramid

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 Isosceles