Triangular tiling

English mathematician John Conway called it a deltille, named from the triangular shape of the Greek letter delta (Δ).

The triangular tiling can also be called a kishextille by a kis operation that adds a center point and triangles to replace the faces of a hextille.

The example shown is 2-uniform, but there are infinitely many such Archimedean colorings that can be created by arbitrary horizontal shifts of the rows.

Putting fewer triangles on a vertex leaves a gap and allows it to be folded into a pyramid.

These can be expanded to Platonic solids: five, four and three triangles on a vertex define an icosahedron, octahedron, and tetrahedron respectively.

This tiling is topologically related as a part of sequence of regular polyhedra with Schläfli symbols {3,n}, continuing into the hyperbolic plane.

It is also topologically related as a part of sequence of Catalan solids with face configuration Vn.6.6, and also continuing into the hyperbolic plane.

A 2-uniform triangular tiling, 4 colored triangles, related to the geodesic polyhedron as {3,6+} 2,0 .
The A *
2 lattice as three triangular tilings: + +