The tetratriangle, or tetri, is a polygon compound composed of 4 triangles. As such it has 12 edges and 12 vertices.
|Bowers style acronym||Tetri|
|Vertex figure||Dyad, length 1|
|Measures (edge length 1)|
|Number of external pieces||24|
|Level of complexity||2|
|Army||Dog, edge length|
|Abstract & topological properties|
|Symmetry||I2(12), order 24|
It is the third stellation of the dodecagon.
Its quotient prismatic equivalent is the triangular tetrahedroorthowedge, which is five-dimensional.
Coordinates for the vertices of a tetratriangle of edge length 1 centered at the origin are given by:
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.
- Bowers, Jonathan. "Regular Polygons and Other Two Dimensional Shapes".