# Tetratriangle

Tetratriangle
Rank2
TypeRegular
SpaceSpherical
Notation
Bowers style acronymTetri
Schläfli symbol{12/4}
Elements
Components4 triangles
Edges12
Vertices12
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt3}{3} ≈ 0.57735}$
Inradius${\displaystyle \frac{\sqrt3}{6} ≈ 0.28868}$
Area${\displaystyle \sqrt3 ≈ 1.73205}$
Angle60°
Central density4
Number of pieces24
Level of complexity2
Related polytopes
ArmyDog
DualTetratriangle
ConjugateTetratriangle
Convex coreDodecagon
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryI2(12), order 24
ConvexNo
NatureTame

The tetratriangle, or tetri, is a polygon compound composed of 4 triangles. As such it has 12 edges and 12 vertices.

It is the third stellation of the dodecagon.

Its quotient prismatic equivalent is the triangular tetrahedroorthowedge, which is five-dimensional.

## Vertex coordinates

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

• ${\displaystyle \left(±\frac12,\,±\frac{\sqrt3}{6}\right),}$
• ${\displaystyle \left(0,\,±\frac{\sqrt3}{3}\right),}$
• ${\displaystyle \left(±\frac{\sqrt3}{6},\,±\frac12\right),}$
• ${\displaystyle \left(±\frac{\sqrt3}{3},\,0\right).}$