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The Coxeter graph is a nonhamiltonian cubic symmetric graph on 28 vertices and 42 edges which can be constructed as illustrated above. It can also be constructed as the graph ...

A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest ...

An n-gonal cupola Q_n is a polyhedron having n obliquely oriented triangular and n rectangular faces separating an {n} and a {2n} regular polygon, each oriented horizontally. ...

For a connected graph G of graph diameter d, the distance-k graph G_k for k=1, ..., d is a graph with the same vertex set and having edge set consisting of the pairs of ...

A compound of five regular dodecahedra with the symmetry of the icosahedron (Wenninger 1983, pp. 145-147) can be constructed by taking a dodecahedron with top and bottom ...

The elongated pentagonal gyrobirotunda is a convex equilateral gyrobirotunda having regular pentagonal upper and lower birotundas arranged rotated 1/10 of a turn with respect ...

The elongated pentagonal orthobirotunda is a convex equilateral orthobirotunda having regular pentagonal upper and lower rotundas arranged symmetrically with respect to each ...

A geometric construction, also called a verging construction, which allows the classical geometric construction rules to be bent in order to permit sliding of a marked ruler. ...

The pentagonal orthobicupola is a convex equilateral orthobicupola having regular pentagonal upper and lower faces. It is Johnson solid J_(30). The unit pentagonal ...

A polygonal diagonal is a line segment connecting two nonadjacent polygon vertices of a polygon. The number of ways a fixed convex n-gon can be divided into triangles by ...