six-fold symmetry axis

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• Symmetry group — Not to be confused with Symmetric group. This article is about the abstract algebraic structures. For other meanings, see Symmetry group (disambiguation). A tetrahedron can be placed in 12 distinct positions by rotation alone. These are… …   Wikipedia

• Tetrahedral symmetry — A regular tetrahedron has 12 rotational (or orientation preserving) symmetries, and a total of 24 symmetries including transformations that combine a reflection and a rotation.The group of symmetries that includes reflections is isomorphic to S 4 …   Wikipedia

• Compound of six pentagonal antiprisms — Type Uniform compound Index UC27 Polyhedra 6 pentagonal antiprisms Faces …   Wikipedia

• Compound of six pentagrammic crossed antiprisms — Type Uniform compound Index UC29 Polyhedra 6 pentagrammic crossed antiprisms F …   Wikipedia

• Uranate — A uranate is a ternary oxide involving the element uranium in one of the oxidation states +4, +5 or +6. A typical chemical formula is MxUyOz, where M represents a cation. The uranium atom in uranates(VI) has two short, co linear, U O bonds and… …   Wikipedia

• Wallpaper group — A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and… …   Wikipedia

• Point groups in three dimensions — In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries… …   Wikipedia

• Crystallographic restriction theorem — The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2 fold, 3 fold, 4 fold, and 6 fold. However, quasicrystals can occur with other symmetries …   Wikipedia

• Quasicrystal — Atomic model of an aluminum palladium manganese (Al Pd Mn) quasicrystal surface. Similar to Fig. 6 in Ref.[1] A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can… …   Wikipedia

• Crystal system — Diamond crystal structure consists of face centered cubic lattice. In crystallography, the terms crystal system, crystal family, and lattice system each refer to one of several classes of space groups, lattices, point groups, or crystals.… …   Wikipedia

• Dihedral group of order 6 — The smallest non abelian group has 6 elements. It is a dihedral group with notation D3 (or D6, both are used) and the symmetric group of degree 3, with notation S3. This page illustrates many group concepts using this group as example. Contents 1 …   Wikipedia