Enumeration of polyhedra
Steven Dutch, Professor Emeritus, Natural and Applied Sciences, University of Wisconsin - Green Bay
How Many polyhedra are There?
polyhedra with 4-7 Faces (1, 2, 7 and 34, respectively)
Non-Convex polyhedra
Explanation of Topological Data for polyhedra
Octahedra
polyhedra with 8 Faces (257 in all). For convenience of access, these are broken down into several files:
Octahedral Nets
Topological Data for Octahedra
Enneahedra
polyhedra with 9 Faces (2606 in all). This set was finally completely enumerated on 2 November 2016. For convenience of access, these are broken down into numerous files:
Enneahedral Nets (7-9 Vertices) 378 total
Topological Data for Enneahedra with 7-9 Vertices
Enneahedral Nets (10 Vertices) 633 total
Topological Data for Enneahedra with 10 Vertices
Enneahedral Nets (11 Vertices) 768 total
Topological Data for Enneahedra with 11 Vertices
- Topological Data for Enneahedra with 11 vertices: 444444444, 333345555 and 333444555
- Topological Data for Enneahedra with 11 vertices: 334444455, 344444445, 333334566, 333335556, and 33334466
- Topological Data for Enneahedra with 11 vertices: 333344556
- Topological Data for Enneahedra with 11 vertices: 333444456
- Topological Data for Enneahedra with 11 vertices: 334444446, 333334467, 333334557, 333344457, 333444447, 333334458 and 333344448
Enneahedral Nets (12 vertices) 558 total
Here it gets ugly. Lots of classes with no unique faces and many requiring multiple views.
Topological Data for Enneahedra with 12 Vertices
- Topological Data for Enneahedra with 12 Vertices: 333455555, 334445555, 334445555, 444444455, 333335666, 333344666, 333345566, 333355556 and 333444566
- Topological Data for Enneahedra with 12 Vertices: 333445556, 334444466, 334444556, 344444456, 444444446 and 333335567
- Topological Data for Enneahedra with 12 Vertices: 333344477, 333344567, 333345557, 333444467, 333444557, 334444457, 344444447, 333335558, 333344468, 333344558 333444458 and 334444448
Enneahedral Nets (13 vertices) 219 total
- Enneahedra with 13 vertices: 334555555, 344455555, 444445555, 333346666 and 333355666 (0-9)
- Enneahedra with 13 vertices: 333445666 (10-22)
- Enneahedra with 13 vertices: 333455566, 333555556 and 334444666 (23-39)
- Enneahedra with 13 vertices: 334445566 (40-64)
- Enneahedra with 13 vertices: 334455556, 344444566,344445556 and 444444566 (65-94)
- Enneahedra with 13 vertices: 333336667, 333345577, 333345667, 333355567 and 333444577 (95-121)
- Enneahedra with 13 vertices: 333444667, 333445567, 333455557 and 334444477 (122-163)
- Enneahedra with 13 vertices: 334444567, 334445557, 344444467, and 344444557 (164-194)
- Enneahedra with 13 vertices: 333345568, 333355558, 333444478, 333444568, 333445558, 334444468, and 334444558 (195-218)
Topological Data for Enneahedra with 13 Vertices
Enneahedral Nets (14 vertices) 50 total
Enneahedra with 14 vertices (0-49)
Topological Data for Enneahedra with 14 Vertices
Topological Data for Enneahedra with 14 Vertices
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Created 23 Sep 1997, Last updated
31 May 2020