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The Fritsch graph is the 9-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

A (general) dodecahedron is a polyhedron having 12 faces. Examples include the Bilinski dodecahedron, decagonal prism, elongated square dipyramid (Johnson solid J_(15)), ...

A pentahedron is polyhedron having five faces. Because there are two pentahedral graphs, there are two convex pentahedra, corresponding to the topologies of the square ...

The Lemoine hexagon is a cyclic hexagon with vertices given by the six concyclic intersections of the parallels of a reference triangle through its symmedian point K. The ...

A deltahedron is a polyhedron whose faces are congruent equilateral triangles (Wells 1986, p. 73). Note that polyhedra whose faces could be triangulated so as to be composed ...

A decahedron is a polyhedron having 10 faces. Examples include the 5-trapezohedron, augmented pentagonal prism (Johnson solid J_(52)), augmented tridiminished icosahedron ...

A parallelohedron is a space-filling polyhedron that fills space using an infinite number of similarly situated copies (Tutton 1964, pp. 567 and 723; Coxeter 1973, pp. ...

The regular hexagon is the regular polygon with six sides, as illustrated above. The inradius r, circumradius R, sagitta s, and area A of a regular hexagon can be computed ...

A heptahedron is a polyhedron with seven faces. Because there are 34 heptahedral graphs, there are 34 topologically distinct convex heptahedra. There are three semiregular ...

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" ...