From Wikipedia, the free encyclopedia
A Gruenbaum-Dress polyhedron is a
regular polyhedron in one of 8 classes in ordinary euclidean space.
8 Classes
- 5
Platonic solids: {3,3}, {3,4}, {4,3}, {3,5}, {5,3}
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- 3
regular tilings: {3,6}, {6,3}, {4,4}
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- 4
Kepler-Poinsot solids: {3,5/2}, {5/2,3}, {5,5/2}, {5/2,5}
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- 3
Coxeter-Petrie polyhedron: {4,6|4}, {6,4|4}, {6,6|3}
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- 9
petrial regular polyhedra (finite skew regular polygons): {3,3}π, {4,3}π, {3,4}π, {5,3}π,{3,5}π {5,5/2}π, {5/2,5}π, {3,5/2}π, {5/2,3}π
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- 6 infinite regular polyhedra with finite skew regular polygons: {4π/3 /1, 3}, {6π/3 /1, 4}, {6π/2 /1, 4}, {10π/3 /1, 5}, {6π/5 /1, 5}, {10π/3 /3, 5/2}, {103π/5 /1, 3}, {10π/5 /3, 3}
- 6 Regular polyhedra with zig-zag polygons
- 9 Polyhedra with helical polygons
TOTAL 45?
References
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Regular polyhedra—old and new Branko Grünbaum aequationes mathematicae February 1977, Volume 16, Issue 1–2, pp 1–20
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A combinatorial theory of Grünbaum's new regular polyhedra, part I: Grünbaum's new regular polyhedra and their automorphism group Andreas W. M. Dress, aequationes mathematicae December 1981, Volume 23, Issue 1, pp 252–265
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[1]
A combinatorial theory of Grünbaum's new regular polyhedra, Part II: Complete enumeration Andreas W.M. Dress Aequationes mathematicae (1985) Volume: 29, page 222-243 ISSN: 0001-9054; 1420-8903/e
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Wythoffian Skeletal Polyhedra in Ordinary Space, I Oct 2016,
Egon Schulte and Abigail Williams
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Polyhedra, Polytopes and Beyond Asia Ivi ́c Weiss