Octagonal pyramid

Octagonal pyramid
Rank	3
Type	CRF
Space	Hyperbolic
Notation
Bowers style acronym	Oppy
Coxeter diagram	ox8oo&#x
Elements
Faces	8 triangles, 1 octagon
Edges	8+8
Vertices	1+8
Vertex figures	1 octagon, edge length 1
	8 isosceles triangles, edge lengths 1, 1, √2+√2
Measures (edge length 1)
Circumradius	$\frac{\sqrt{-\sqrt{2}}}{2} ≈ 0.59460 i$
Volume	$\frac{\sqrt{-8-6\sqrt{2}}}{3} ≈ 1.35340 i$
Height	$\sqrt{-\frac{\sqrt{2}}{2}} ≈ 0.84090 i$
Related polytopes
Army	Oppy
Regiment	Oppy
Dual	Octagonal pyramid
Abstract & topological properties
Flag count	64
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	I2×I, order 16
Convex	Yes
Net count	144

The octagonal pyramid, or oppy, is a pyramid with a octagonal base and 8 triangles as sides. The version with equilateral triangles as sides is hyperbolic, and is the vertex-first cap of the order-8 triangular tiling. Other variants with isosceles triangles as sides exist, that can be embedded in 3D euclidean space.