Tetratriangle

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

Variations
The tetratriangle can be varied by seeing it as a compound of 2 hexagrams and changing the angle between the two component hexagrams from the usual 30°. These 4-triangle compounds generally have a dihexagon as their convex hull and remain uniform, but not regular, with hexagonal symmetry only.