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This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger. The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes.
The Jahn–Teller effect (JT effect or JTE) is an important mechanism of spontaneous symmetry breaking in molecular and solid-state systems which has far-reaching consequences in different fields, and is responsible for a variety of phenomena in spectroscopy, stereochemistry, crystal chemistry, molecular and solid-state physics, and materials science.
O h, *432, [4,3], or m3m of order 48 – achiral octahedral symmetry or full octahedral symmetry. This group has the same rotation axes as O, but with mirror planes, comprising both the mirror planes of T d and T h. This group is isomorphic to S 4.C 2, and is the full symmetry group of the cube and octahedron. It is the hyperoctahedral group ...
A perfect octahedron belongs to the point group O h. Examples of octahedral compounds are sulfur hexafluoride SF 6 and molybdenum hexacarbonyl Mo(CO) 6 . The term "octahedral" is used somewhat loosely by chemists, focusing on the geometry of the bonds to the central atom and not considering differences among the ligands themselves.
The Geometrical Foundation of Natural Structure: A source book of Design. pp. 142– 144, Figure 4-49, 50, 51 Custers of 12 spheres, 42 spheres, 92 spheres. Pugh, Antony (1976). "Chapter 6. The Geodesic Polyhedra of R. Buckminster Fuller and Related Polyhedra". Polyhedra: a visual approach. Wenninger, Magnus (1979). Spherical Models.
The ideal tetrahedron, cube, octahedron, and dodecahedron form respectively the order-6 tetrahedral honeycomb, order-6 cubic honeycomb, order-4 octahedral honeycomb, and order-6 dodecahedral honeycomb; here the order refers to the number of cells meeting at each edge. However, the ideal icosahedron does not tile space in the same way.
o o o s. c: o thO 00 . Created Date: 9/20/2007 3:37:18 PM
Picture Name Schläfli symbol Vertex/Face configuration exact dihedral angle (radians) dihedral angle – exact in bold, else approximate (degrees) Platonic solids (regular convex)