User:Tomruen/Grünbaum-Dress polyhedron

A Gruenbaum-Dress polyhedron is a regular polyhedron in one of 8 classes in ordinary euclidean space.

8 Classes

1. 5 Platonic solids: {3,3}, {3,4}, {4,3}, {3,5}, {5,3}

   

2. 3 regular tilings: {3,6}, {6,3}, {4,4}

   

3. 4 Kepler-Poinsot solids: {3,5/2}, {5/2,3}, {5,5/2}, {5/2,5}

   

4. 3 Coxeter-Petrie polyhedron: {4,6|4}, {6,4|4}, {6,6|3}

   

5. 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

   

6. 6 infinite regular polyhedra with finite skew regular polygons: {4^π/3 /1, 3}, {6^π/3 /1, 4}, {6^π/2 /1, 4}, {10^π/3 /1, 5}, {6^π/5 /1, 5}, {10^π/3 /3, 5/2}, {10^3π/5 /1, 3}, {10^π/5 /3, 3}
7. 6 Regular polyhedra with zig-zag polygons
8. 9 Polyhedra with helical polygons

TOTAL 45?

References

• Regular polyhedra—old and new Branko Grünbaum aequationes mathematicae February 1977, Volume 16, Issue 1–2, pp 1–20
• [230,%22panX%22:0.49,%22panY%22:0.809,%22view%22:%22info%22,%22zoom%22:0.339}] 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
• [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
• Wythoffian Skeletal Polyhedra in Ordinary Space, I Oct 2016, Egon Schulte and Abigail Williams
• Polyhedra, Polytopes and Beyond Asia Ivi ́c Weiss