Chiral Polyhedra in Ordinary Space, I
نویسندگان
چکیده
منابع مشابه
Chiral Polyhedra in Ordinary Space, I
Chiral polyhedra in ordinary euclidean space E3 are nearly regular polyhedra; their geometric symmetry groups have two orbits on the flags, such that adjacent flags are in distinct orbits. This paper completely enumerates the discrete infinite chiral polyhedra in E3 with finite skew faces and finite skew vertex-figures. There are several families of such polyhedra of types {4, 6}, {6, 4} and {6...
متن کاملChiral Polyhedra in Ordinary Space, II
A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary Euclidean space E3 with finite skew faces and finite skew vertex-figures; they occur in infinite families and are of types {4, 6}, {6, 4} and {6, 6}. Part II completes the enumeration of all disc...
متن کاملJ an 2 00 5 Chiral polyhedra in ordinary space , II ∗
A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary Euclidean space E3 with finite skew faces and finite skew vertex-figures; they occur in infinite families and are of types {4, 6}, {6, 4} and {6, 6}. Part II completes the enumeration of all disc...
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We enumerate the regular and chiral polyhedra (in the sense of Grünbaum’s skeletal approach) whose vertex and edge sets are a subset of those of the primitive cubic lattice, the face-centred cubic lattice, or the body-centred cubic lattice.
متن کاملRegular Polytopes in Ordinary Space
The three aims of this paper are to obtain the proof by Dress of the completeness of the enumeration of the Grünbaum–Dress polyhedra (that is, the regular apeirohedra, or apeirotopes of rank 3) in ordinary space E3 in a quicker and more perspicuous way, to give presentations of those of their symmetry groups which are affinely irreducible, and to describe all the discrete regular apeirotopes of...
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ژورنال
عنوان ژورنال: Discrete and Computational Geometry
سال: 2004
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-004-0843-x