Tetrahedral Symmetry
01: tetrahedron (3|2 3)
02: truncated tetrahedron (2 3|3)
03: octahemioctahedron (3/2 3|3)
04: tetrahemihexahedron (3/2 3|2)

Octahedral Symmetry
05: octahedron (4|2 3)
06: cube (3|2 4)
07: cuboctahedron (2|3 4)
08: truncated octahedron (2 4|3)
09: truncated cube (2 3|4)
10: rhombicuboctahedron (3 4|2)
11: truncated cuboctahedron (2 3 4|)
12: snub cube (|2 3 4)
13: small cubicuboctahedron (3/2 4|4)
14: great cubicuboctahedron (3 4|4/3)
15: cubohemioctahedron (4/3 4|3)
16: cubitruncated cuboctahedron (4/3 3 4|)
17: great rhombicuboctahedron (3/2 4|2)
18: small rhombihexahedron (3/2 2 4|)
19: stellated truncated hexahedron (2 3|4/3)
20: great truncated cuboctahedron (4/3 2 3|)
21: great rhombihexahedron (4/3 3/2 2|)

Icosahedral Symmetry
22: icosahedron (5|2 3)
23: dodecahedron (3|2 5)
24: icosidodecahedron (2|3 5)
25: truncated icosahedron (2 5|3)
26: truncated dodecahedron (2 3|5)
27: rhombicosidodecahedron (3 5|2)
28: truncated icosidodecahedron (2 3 5|)
29: snub dodecahedron (|2 3 5)
30: small ditrigonal icosidodecahedron (3|5/2 3)
31: small icosicosidodecahedron (5/2 3|3)
32: small snub icosicosidodecahedron (|5/2 3 3)
33: small dodecicosidodecahedron (3/2 5|5)
34: small stellated dodecahedron (5|2 5/2)
35: great dodecahedron (5/2|2 5)
36: dodecadodecahedron (2|5/2 5)
37: truncated great dodecahedron (2 5/2|5)
38: rhombidodecadodecahedron (5/2 5|2)
39: small rhombidodecahedron (2 5/2 5|)
40: snub dodecadodecahedron (|2 5/2 5)
41: ditrigonal dodecadodecahedron (3|5/3 5)
42: great ditrigonal dodecicosidodecahedron (3 5|5/3)
43: small ditrigonal dodecicosidodecahedron (5/3 3|5)
44: icosidodecadodecahedron (5/3 5|3)
45: icositruncated dodecadodecahedron (5/3 3 5|)
46: snub icosidodecadodecahedron (|5/3 3 5)
47: great ditrigonal icosidodecahedron (3/2|3 5)
48: great icosicosidodecahedron (3/2 5|3)
49: small icosihemidodecahedron (3/2 3|5)
50: small dodecicosahedron (3/2 3 5|)
51: small dodecahemidodecahedron (5/4 5|5)
52: great stellated dodecahedron (3|2 5/2)
53: great icosahedron (5/2|2 3)
54: great icosidodecahedron (2|5/2 3)
55: great truncated icosahedron (2 5/2|3)
56: rhombicosahedron (2 5/2 3|)
57: great snub icosidodecahedron (|2 5/2 3)
58: small stellated truncated dodecahedron (2 5|5/3)
59: truncated dodecadodecahedron (5/3 2 5|)
60: inverted snub dodecadodecahedron (|5/3 2 5)
61: great dodecicosidodecahedron (5/2 3|5/3)
62: small dodecahemicosahedron (5/3 5/2|3)
63: great dodecicosahedron (5/3 5/2 3|)
64: great snub dodecicosidodecahedron (|5/3 5/2 3)
65: great dodecahemicosahedron (5/4 5|3)
66: great stellated truncated dodecahedron (2 3|5/3)
67: great rhombicosidodecahedron (5/3 3|2)
68: great truncated icosidodecahedron (5/3 2 3|)
69: great inverted snub icosidodecahedron (|5/3 2 3)
70: great dodecahemidodecahedron (5/3 5/2|5/3)
71: great icosihemidodecahedron (3/2 3|5/3)
72: small retrosnub icosicosidodecahedron (|3/2 3/2 5/2)
73: great rhombidodecahedron (3/2 5/3 2|)
74: great retrosnub icosidodecahedron (|3/2 5/3 2)
75: great dirhombicosidodecahedron (|3/2 5/3 3 5/2)

Dihedral Symmetry
These examples have five fold symmetry. There are such polyhedra for each n > 2.
76: pentagonal prism (2 5|2)
77: pentagonal antiprism (|2 2 5)
78: pentagrammic prism (2 5/2|2)
79: pentagrammic antiprism (|2 2 5/2)
80: pentagrammic crossed antiprism (|2 2 5/3)