- Source: List of uniform polyhedra by spherical triangle
- Daftar masalah matematika yang belum terpecahkan
- List of uniform polyhedra by spherical triangle
- List of uniform polyhedra by Schwarz triangle
- Uniform star polyhedron
- Uniform polyhedron
- Polyhedron
- List of mathematical shapes
- Truncated icosahedron
- Equilateral triangle
- Platonic solid
- Lists of uniform tilings on the sphere, plane, and hyperbolic plane
There are many relations among the uniform polyhedra. This List of uniform polyhedra by spherical triangle groups them by the Wythoff symbol.
Key
The vertex figure can be discovered by considering the Wythoff symbol:
p|q r - 2p edges, alternating q-gons and r-gons. Vertex figure (q.r)p.
p|q 2 - p edges, q-gons (here r=2 so the r-gons are degenerate lines).
2|q r - 4 edges, alternating q-gons and r-gons
q r|p - 4 edges, 2p-gons, q-gons, 2p-gons r-gons, Vertex figure 2p.q.2p.r.
q 2|p - 3 edges, 2p-gons, q-gons, 2p-gons, Vertex figure 2p.q.2p.
p q r|- 3 edges, 2p-gons, 2q-gons, 2r-gons, vertex figure 2p.2q.2r
Convex
Non-convex
= a b 2
=3 3 2
a
π
3
b
π
3
c
π
2
{\displaystyle {a\pi \over 3}\ {b\pi \over 3}\ {c\pi \over 2}}
Group
4 3 2
a
π
4
b
π
3
c
π
2
{\displaystyle {a\pi \over 4}\ {b\pi \over 3}\ {c\pi \over 2}}
Group
5 3 2
a
π
5
b
π
3
c
π
2
{\displaystyle {a\pi \over 5}\ {b\pi \over 3}\ {c\pi \over 2}}
Group
5 5 2
a
π
5
b
π
5
c
π
2
{\displaystyle {a\pi \over 5}\ {b\pi \over 5}\ {c\pi \over 2}}
Group
= a b 3
=3 3 3
a
π
3
b
π
3
c
π
3
{\displaystyle {a\pi \over 3}\ {b\pi \over 3}\ {c\pi \over 3}}
Group
4 3 3
a
π
4
b
π
3
c
π
3
{\displaystyle {a\pi \over 4}\ {b\pi \over 3}\ {c\pi \over 3}}
Group
5 3 3
a
π
5
b
π
3
c
π
3
{\displaystyle {a\pi \over 5}\ {b\pi \over 3}\ {c\pi \over 3}}
Group
4 4 3
a
π
4
b
π
4
c
π
3
{\displaystyle {a\pi \over 4}\ {b\pi \over 4}\ {c\pi \over 3}}
Group
5 5 3
a
π
5
b
π
5
c
π
3
{\displaystyle {a\pi \over 5}\ {b\pi \over 5}\ {c\pi \over 3}}
Group
= a b 5
=5 5 5
a
π
5
b
π
5
c
π
5
{\displaystyle {a\pi \over 5}\ {b\pi \over 5}\ {c\pi \over 5}}
Group