# Trisquare

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

Trisquare
Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymTrisquare
Schläfli symbol{12/3}
Elements
Components3 squares
Edges12
Vertices12
Vertex figureDyad, length 2
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt2}{2} ≈ 0.70711}$
Inradius${\displaystyle \frac12 = 0.5}$
Area3
Angle90°
Central density3
Number of external pieces24
Level of complexity2
Related polytopes
ArmyDog, edge length ${\displaystyle \frac{\sqrt3-1}{2}}$
DualTrisquare
ConjugateTrisquare
Convex coreDodecagon
Abstract & topological properties
Flag count24
Euler characteristic0
OrientableYes
Properties
SymmetryI2(12), order 24
ConvexNo
NatureTame

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:

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