Quasiregular

2007, V. A. Blatov, O. Delgado-Friedrichs, M. O'Keeffe, D. M. Proserpio, Periodic nets and tilings: possibilities tor analysis and design of porous materials: Proceedings of the 15th International Zeolite Conference, Ruren Xu, Jiesheng Chen, Zi Gao, Wenfu Yan (editors), From Zeolites to Porous MOF Materials, page 1642, If we allow the coordination figure to be a quasiregular polyhedron (a polyhedron with one kind of vertex and edge, but two kinds of face) there is just one possibility compatible with translational symmetry – a cuboctahedron.

The lattice points that lie in this plane are the vertices of the regular tessellation {3, 4} of equilateral triangles, and the other points just mentioned are the vertices of the quasiregular tessellation #92;begin#123;Bmatrix#125;3#92;#92;4#92;end#123;Bmatrix#125; of triangles and hexagons [9, p. 60].

There are two quasiregular polyhedra not having identical regular faces: the cuboctahedron (dymaxion) and the icosidodecahedron.

Two semiregular polyhedra are classified as so-called quasiregular polyhedra. They have two kinds of faces, and each face of one kind is entirely surrounded by faces of the other kind.

The element a can be uniquely represented in the form r + t, where [rt] = 0, t is nilpotent and r is a quasiregular element of G ([1]; p. 108).

A onesided ideal is quasiregular provided that it consists of quasiregular elements.

A norm #92;begin#123;Vmatrix#125;#92;end#123;Vmatrix#125; is called spectral if the group of quasiregular elements is open in the associated norm topology, equivalently if it satisfies Gelfand's spectral radius formula:[…].

1999, S. Mueller, Variational models for microstructure and phase transitions, F. Bethuel, G. Huisken, S. Mueller, K. Steffen (editors),Calculus of Variations and Geometric Evolution Problems, Springer, Lecture Notes in Mathematics, Volume 1713, page 108, An alternative proof that features an interesting connection with the theory of quasiconformal (or more precisely quasiregular) maps proceeds as follows.