Examples
All the regular and semiregular polyhedra can be projected onto the sphere as tilings. Given by their Schläfli symbol {p, q} or vertex figure (a.b.c. ...):
| (p q r) | {p,q} | (q.2p.2p) | (p.q.p.q) | (p. 2q.2q) | {q,p} | (q.4.p. 4) | (2r.2q.2p) | (3.r.3.q.3.p) |
|---|---|---|---|---|---|---|---|---|
| Tetrahedral (3 3 2) |
{3,3} |
(3.6.6) |
(3.3.3.3) |
(3.6.6) |
{3,3} |
(3.4.3.4) |
(4.6.6) |
(3.2.3.3.3.3) |
| Octahedral (4 3 2) |
{4,3} |
(3.8.8) |
(3.4.3.4) |
(4.6.6) |
{3,4} |
(3.4.4.4) |
(4.6.8) |
(3.2.3.3.3.4) |
| Icosahedral (5 3 2) |
{5,3} |
(3.10.10) |
(3.5.3.5) |
(5.6.6) |
{3,5} |
(3.4.5.4) |
(4.6.10) |
(3.2.3.3.3.5) |
| Dihedral (6 2 2) example |
{6,2} |
(2.12.12) |
(2.6.2.6) |
(6.4.4) |
{2,6} |
(2.4.6.4) |
(4.4.12) |
(3.2.3.2.3.6) |
Read more about this topic: Spherical Polyhedron
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