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The polytopes of rank 2 (2-polytopes) are called polygons. Regular polygons are equilateral and cyclic. A p-gonal regular polygon is represented by Schläfli symbol {p}. Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular. They use the same vertices as the convex forms, but ...
A new figure is obtained by rotating these regular n/m-gons one vertex to the left on the original polygon until the number of vertices rotated equals n/m minus one, and combining these figures. An extreme case of this is where n / m is 2, producing a figure consisting of n /2 straight line segments; this is called a degenerate star polygon .
A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples.
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.In particular, all its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are themselves regular polytopes of dimension j≤ n.
or Category:4-polytopes: For Polyteron or Polytera: see 5-polytope: or Category:5-polytopes: For Polypeton or Polypeta: see 6-polytope: or Category:6-polytopes: For Polyexon or Polyexa: see 7-polytope: or Category:7-polytopes: For Polyzetton or Polyzetta: see 8-polytope: or Category:8-polytopes: For Polyyotton or Polyyotta: see 9-polytope: or ...
Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions n as an n-dimensional polytope or n-polytope. For example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope.
Pages in category "Regular polytopes" The following 6 pages are in this category, out of 6 total. This list may not reflect recent changes. ...
The following table lists some properties of the six convex regular 4-polytopes. The symmetry groups of these 4-polytopes are all Coxeter groups and given in the notation described in that article. The number following the name of the group is the order of the group.