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 |
Read more about this topic: Triangular Tiling
Famous quotes containing the word related:
“In the middle years of childhood, it is more important to keep alive and glowing the interest in finding out and to support this interest with skills and techniques related to the process of finding out than to specify any particular piece of subject matter as inviolate.”
—Dorothy H. Cohen (20th century)