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A self-dual graphs is a graph that is dual to itself. Wheel graphs are self-dual, as are the examples illustrated above. Naturally, the skeleton of a self-dual polyhedron is ...

A spherical sector is a solid of revolution enclosed by two radii from the center of a sphere. The spherical sector may either be "open" and have a conical hole (left figure; ...

The moment of inertia with respect to a given axis of a solid body with density rho(r) is defined by the volume integral I=intrho(r)r__|_^2dV, (1) where r__|_ is the ...

An attractive compound can be constructed of 6 pentagonal prisms having unit edge lengths, as illustrated above. A net for the solid is illustrated above, where s_1 = ...

Bilinski (1960) noted that by collapsing any one of the five zones of the rhombic icosahedron, a second rhombic dodecahedron distinct from the dual polyhedron of the ...

The tetragonal antiwedge is the topological class of hexahedron. It has 10 edges and 6 vertices and its faces consist of 4 triangles and 2 quadrilaterals. A tetragonal ...

A Hamiltonian path, also called a Hamilton path, is a graph path between two vertices of a graph that visits each vertex exactly once. If a Hamiltonian path exists whose ...

The Simson line is the line containing the feet P_1, P_2, and P_3 of the perpendiculars from an arbitrary point P on the circumcircle of a triangle to the sides or their ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

The truncated icosahedron is the 32-faced Archimedean solid with 60 vertices corresponding to the facial arrangement 20{6}+12{5}. It is also the uniform polyhedron with ...