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In general, an icosidodecahedron is a 32-faced polyhedron. A number of such solids are illustrated above. "The" (quasiregular) icosidodecahedron is the 32-faced Archimedean ...

"Escher's solid" is the solid illustrated on the right pedestal in M. C. Escher's Waterfall woodcut (Bool et al. 1982, p. 323). It is obtained by augmenting a rhombic ...

The Gömböc (meaning "sphere-like" in Hungarian) is the name given to a class of convex solids which possess a unique stable and a unique unstable point of equilibrium. ...

An isohedron is a convex polyhedron with symmetries acting transitively on its faces with respect to the center of gravity. Every isohedron has an even number of faces ...

The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" ...

There are at least 15 classes of convex pentagonal tilings, as illustrated above. The first five were discovered during investigations of German mathematician Karl Reinhardt ...

The ten-of-diamonds decahedron is a stereohedron and space-filling polyhedron on 8 vertices, 16 edges, and 10 faces (8 of which are non-equilateral triangles and two of which ...

A generalized quadrangle is a generalized polygon of order 4. An order-(s,t) generalized quadrangle contains s+1 points in each line and has t+1 lines through every point, ...

A regular pyramid is a right pyramid whose base is a regular polygon. For a right pyramid of height h with a regular n-gonal base of side length a and circumradius R, the ...

The points of intersection of the adjacent angle trisectors of the angles of any triangle DeltaABC are the polygon vertices of an equilateral triangle DeltaDEF known as the ...