Compound of eight digons

Compound of eight digons
Rank	2
Type	Regular
Notation
Schläfli symbol	{16/8}
Elements
Components	8 digons
Edges	16
Vertices	16
Vertex figure	Dyad, length 0
Measures (edge length 1)
Circumradius	${\frac {1}{2}}=0.5$
Area	0
Angle	0°
Central density	8
Related polytopes
Army	Hed, edge length ${\frac {\sqrt {2-{\sqrt {2+{\sqrt {2}}}}}}{2}}$
Dual	Compound of eight digons
Conjugate	Compound of eight digons
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	I2(16), order 28
Convex	No
Nature	Tame

The compound of eight digons is a degenerate regular polygon compound, being the compound of 8 digons. As such it has 16 edges and 16 vertices.

It can be formed as a degenerate stellation of the hexadecagon, by extending the edges to infinity.

Its quotient prismatic equivalent is the digonal octaexoorthowedge, which is nine-dimensional.

Vertex coordinates

The vertices of a compound of eight digons of edge length 1 are given by all permutations of:

• $\left(\pm {\frac {\sqrt {2-{\sqrt {2+{\sqrt {2}}}}}}{2}},\,\pm {\frac {\sqrt {2+{\sqrt {2+{\sqrt {2}}}}}}{2}}\right),$
• $\left(\pm {\frac {\sqrt {2-{\sqrt {2-{\sqrt {2}}}}}}{2}},\,\pm {\frac {\sqrt {2+{\sqrt {2-{\sqrt {2}}}}}}{2}}\right).$