# Compound of three squares

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

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

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:

• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{2}},\,0\right),}$
• ${\displaystyle \left(0,\,\pm {\frac {\sqrt {2}}{2}}\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{4}},\,\pm {\frac {\sqrt {6}}{4}}\right),}$
• ${\displaystyle \left(\pm {\frac {\sqrt {6}}{4}},\,\pm {\frac {\sqrt {2}}{4}}\right).}$