Stellated octagon

Stellated octagon
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Soc
Coxeter diagram	xo4ox
Schläfli symbol	{8/2}
Elements
Components	2 squares
Edges	8
Vertices	8
Vertex figure	Dyad, length √2
Measures (edge length 1)
Circumradius	$\frac{\sqrt2}{2} ≈ 0.70711$
Inradius	$\frac12 = 0.5$
Area	2
Angle	90°
Central density	2
Number of external pieces	16
Level of complexity	2
Related polytopes
Army	Oc, edge length $\sqrt{\frac{2-\sqrt2}{2}}$
Dual	Stellated octagon
Conjugate	Stellated octagon
Convex core	Octagon
Abstract & topological properties
Flag count	16
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(8), order 16
Convex	No
Nature	Tame

The stellated octagon, or soc is a polygon compound composed of two squares. As such it has 8 edges and 8 vertices.

It is the first stellation of the octagon.

Its quotient prismatic equivalent is the square antiprism, which is three-dimensional.

Vertex coordinates

Coordinates for the vertices of a stellated octagon of edge length 1 centered at the origin are given by:

• $\left(±\frac12,\,±\frac12\right),$
• $\left(±\frac{\sqrt2}{2},\,0\right),$
• $\left(0,\,±\frac{\sqrt2}{2}\right).$

Variations

The stellated octagon can be varied by changing the angle between the two component squares from the usual 45°. These 2-square compounds generally have a ditetragon as their convex hull and remain uniform, but not regular, with square symmetry only.

External links

• Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".