Trisquare

The trisquare is a polygon compound composed of 3 squares. As such it has 12 edges and 12 vertices.

Trisquare
(OFF file)
Rank	2
Type	Regular
Space	Spherical
Notation
Bowers style acronym	Trisquare
Schläfli symbol	{12/3}
Elements
Components	3 squares
Edges	12
Vertices	12
Vertex figure	Dyad, length √2
Measures (edge length 1)
Circumradius	$\frac{\sqrt2}{2} ≈ 0.70711$
Inradius	$\frac12 = 0.5$
Area	3
Angle	90°
Central density	3
Number of external pieces	24
Level of complexity	2
Related polytopes
Army	Dog, edge length $\frac{\sqrt3-1}{2}$
Dual	Trisquare
Conjugate	Trisquare
Convex core	Dodecagon
Abstract & topological properties
Flag count	24
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(12), order 24
Convex	No
Nature	Tame

It is the second stellation of the dodecagon.

Its quotient prismatic equivalent is the 12-4 step prism, which is four-dimensional.

Vertex coordinates

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

• $\left(±\frac{\sqrt2}{2},\,0\right),$
• $\left(0,\,±\frac{\sqrt2}{2}\right),$
• $\left(±\frac{\sqrt2}{4},\,±\frac{\sqrt6}{4}\right),$
• $\left(±\frac{\sqrt6}{4}, \,±\frac{\sqrt2}{4}\right).$

External links

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