Triangular Tiling - Related Polyhedra and Tilings

Related Polyhedra and Tilings

The planar tilings are related to polyhedra. 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.

{3,3}

{3,4}

{3,5}

{3,6}

{3,7}

{3,8}

{3,9}

...

(3,∞}

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.

V3.6.6

V4.6.6

V5.6.6

V6.6.6

V7.6.6

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