Regular and Chiral Polyhedra in Euclidean Nets
نویسنده
چکیده
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.
منابع مشابه
Polyhedra, complexes, nets and symmetry.
Skeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial and algebraic properties. They can be viewed as finite or infinite 3-periodic graphs (nets) equipped with additional structure imposed by the faces, allowed to be skew, zigzag or helical. A polyhedron or complex is regular if its geometr...
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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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ورودعنوان ژورنال:
- Symmetry
دوره 8 شماره
صفحات -
تاریخ انتشار 2016