Polyhedra

Some articles on polyhedra:

Antiparallelogram - Uniform Polyhedra and Their Duals
... Several nonconvex uniform polyhedra, including the tetrahemihexahedron, cubohemioctahedron, octahemioctahedron, small rhombihexahedron, small ... For uniform polyhedra of this type in which the faces do not pass through the center point of the polyhedron, the dual polyhedron has antiparallelograms as its faces ... The antiparallelograms that form the faces of these dual uniform polyhedra are the same antiparallelograms that form the vertex figure of the original uniform polyhedron ...
Symmetric Chiral Polytopes - In Three Dimensions
... The quasiregular polyhedra and their duals, such as the cuboctahedron and the rhombic dodecahedron, provide another interesting type of near-miss they have two orbits of flags, but are mirror-symmetric, and not ... However, despite the nonexistence of finite chiral three-dimensional polyhedra, there exist infinite three-dimensional chiral skew polyhedra of types {4,6}, {6,4}, and {6,6} ...
Schönhardt Polyhedron - Related Constructions
... Rambau (2005) that the Schönhardt polyhedron can be generalized to other polyhedra, combinatorially equivalent to antiprisms, that cannot be triangulated ... These polyhedra are formed by connecting regular k-gons in two parallel planes, twisted with respect to each other, in such a way that k of the 2k ... and the Császár polyhedron have no diagonals at all every pair of vertices in these polyhedra forms an edge ...
Spherical Polyhedron
... Much of the theory of symmetrical polyhedra is most conveniently derived in this way ... Some polyhedra, such as the hosohedra and their duals the dihedra, exist as spherical polyhedra but have no flat-faced analogue ...
Strip Algebra
... structures, considered as a subgroup of polyhedra, and more precisely, of polyhedra with vertices formed by three edges ... This restriction is imposed on the polyhedra because carbon nanotubes are formed of sp2 carbon atoms ...