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.

Hexagonal pyramid
Hexagonal pyramid.png
Faces6 triangles
1 hexagon
Vertex configuration6(32.6)
Schläfli symbol( ) ∨ {6}
Symmetry groupC6v, [6], (*66)
Rotation groupC6, [6]+, (66)
Dual polyhedronSelf-dual
Geometric Net of an Hexagonal Pyramid.svg

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 coordinatesEdit

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


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


STL Hexagonal pyramid

A hexagonal pyramid has the following Coxeter diagrams:

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

Related polyhedraEdit

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

See alsoEdit

External linksEdit

  • Weisstein, Eric W. "Hexagonal Pyramid". MathWorld.
  • Virtual Reality Polyhedra www.georgehart.com: The Encyclopedia of Polyhedra
  • Conway Notation for Polyhedra Try: "Y6"
  • [1] Hexagonal pyramid - Polytope Wiki