Hexagonal pyramid

Hexagonal pyramid
Rank	3
Type	CRF
Space	Euclidean
Notation
Bowers style acronym	Hippy
Coxeter diagram	ox6oo&#x
Elements
Faces	6 triangles, 1 hexagon
Edges	6+6
Vertices	1+6
Vertex figures	1 hexagon, edge length 1
	6 isosceles triangles, edge lengths 1, 1, √3
Measures (edge length 1)
Circumradius	∞
Volume	0
Dihedral angles	3-3: 180º
	3-6: 0º
Height	0
Related polytopes
Army	Hippy
Regiment	Hippy
Dual	Hexagonal pyramid
Conjugate	None
Abstract & topological properties
Flag count	48
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	G2×I, order 12
Convex	Yes
Net count	32

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 non-degenerate polyhedra.

It is the vertex-first cap of the triangular 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)

External links

• Klitzing, Richard. "hippy".

• Wikipedia Contributors. "Hexagonal pyramid".