In geometry , a 7ORTHOPLEX, or 7cross polytope , is a regular
7polytope
It has two constructed forms, the first being regular with Schläfli
symbol {35,4}, and the second with alternately labeled
(checkerboarded) facets, with
Schläfli symbol
It is a part of an infinite family of polytopes, called crosspolytopes or orthoplexes. The dual polytope is the 7hypercube , or hepteract . CONTENTS * 1 Alternate names * 2 Images * 3 Construction * 4 Cartesian coordinates * 5 See also * 6 References * 7 External links ALTERNATE NAMES * HEPTACROSS, derived from combining the family name cross polytope
with hept for seven (dimensions) in Greek .
* HECATONICOSOCTAEXON as a 128facetted
7polytope
IMAGES orthographic projections COXETER PLANE B7 / A6 B6 / D7 B5 / D6 / A4 GRAPH DIHEDRAL SYMMETRY COXETER PLANE B4 / D5 B3 / D4 / A2 B2 / D3 GRAPH DIHEDRAL SYMMETRY COXETER PLANE A5 A3 GRAPH DIHEDRAL SYMMETRY CONSTRUCTION There are two Coxeter groups associated with the 7orthoplex, one
regular , dual of the hepteract with the C7 or symmetry group, and a
half symmetry with two copies of
6simplex
