In 7-dimensional geometry , a
CONTENTS * 1 Alternate names * 2 Coordinates * 3 Images * 4 Related polytopes * 5 Notes * 6 External links ALTERNATE NAMES It can also be called an OCTAEXON, or OCTA-7-TOPE, as an 8-facetted polytope in 7-dimensions. The name octaexon is derived from octa for eight facets in Greek and -ex for having six-dimensional facets, and -on. Jonathan Bowers gives an octaexon the acronym OCA. COORDINATES The Cartesian coordinates of the vertices of an origin-centered regular octaexon having edge length 2 are: ( 1 / 28 , 1 / 21 , 1 / 15 , 1 / 10 , 1 / 6 , 1 / 3 , 1 ) {displaystyle left({sqrt {1/28}}, {sqrt {1/21}}, {sqrt {1/15}}, {sqrt {1/10}}, {sqrt {1/6}}, {sqrt {1/3}}, pm 1right)} ( 1 / 28 , 1 / 21 , 1 / 15 , 1 / 10 , 1 / 6 , 2 1 / 3 , 0 ) {displaystyle left({sqrt {1/28}}, {sqrt {1/21}}, {sqrt {1/15}}, {sqrt {1/10}}, {sqrt {1/6}}, -2{sqrt {1/3}}, 0right)} ( 1 / 28 , 1 / 21 , 1 / 15 , 1 / 10 , 3 / 2 , 0 , 0 ) {displaystyle left({sqrt {1/28}}, {sqrt {1/21}}, {sqrt {1/15}}, {sqrt {1/10}}, -{sqrt {3/2}}, 0, 0right)} ( 1 / 28 , 1 / 21 , 1 / 15 , 2 2 / 5 , 0 , 0 , 0 ) {displaystyle left({sqrt {1/28}}, {sqrt {1/21}}, {sqrt {1/15}}, -2{sqrt {2/5}}, 0, 0, 0right)} ( 1 / 28 , 1 / 21 , 5 / 3 , 0 , 0 , 0 , 0 ) {displaystyle left({sqrt {1/28}}, {sqrt {1/21}}, -{sqrt {5/3}}, 0, 0, 0, 0right)} ( 1 / 28 , 12 / 7 , 0 , 0 , 0 , 0 , 0 ) {displaystyle left({sqrt {1/28}}, -{sqrt {12/7}}, 0, 0, 0, 0, 0right)} ( 7 / 4 , 0 , 0 , 0 , 0 , 0 , 0 ) {displaystyle left(-{sqrt {7/4}}, 0, 0, 0, 0, 0, 0right)} More simply, the vertices of the
IMAGES 7-
Model created using straws (edges) and plasticine balls (vertices) in
triakis tetrahedral envelope
7-
orthographic projections AK COXETER PLANE A7 A6 A5 GRAPH DIHEDRAL SYMMETRY AK COXETER PLANE A4 A3 A2 GRAPH DIHEDRAL SYMMETRY RELATED POLYTOPES This polytope is a facet in the uniform tessellation 331 with
This polytope is one of 71 uniform 7-polytopes with A7 symmetry. A7 POLYTOPES t0 t1 t2 t3 t0,1 t0,2 t1,2 t0,3 t1,3 t2,3 t0,4 t1,4 t2,4 t0,5 t1,5 t0,6 t0,1,2 t0,1,3 t0,2,3 t1,2,3 t0,1,4 t0,2,4 t1,2,4 t0,3,4 t1,3,4 t2,3,4 t0,1,5 t0,2,5 t1,2,5 t0,3,5 t1,3,5 t0,4,5 t0,1,6 t0,2,6 t0,3,6 t0,1,2,3 t0,1,2,4 t0,1,3,4 t0,2,3,4 t1,2,3,4 t0,1,2,5 t0,1,3,5 t0,2,3,5 t1,2,3,5 t0,1,4,5 t0,2,4,5 t1,2,4,5 t0,3,4,5 t0,1,2,6 t0,1,3,6 t0,2,3,6 t0,1,4,6 t0,2,4,6 t0,1,5,6 t0,1,2,3,4 t0,1,2,3,5 t0,1,2,4,5 t0,1,3,4,5 t0,2,3,4,5 t1,2,3,4,5 t0,1,2,3,6 t0,1,2,4,6 t0,1,3,4,6 t0,2,3,4,6 t0,1,2,5,6 t0,1,3,5,6 t0,1,2,3,4,5 t0,1,2,3,4,6 t0,1,2,3,5,6 t0,1,2,4,5,6 t0,1,2,3,4,5,6 NOTES * ^ Klitzing, Richard. "7D uniform polytopes (polyexa) x3o3o3o3o3o - oca". |