Heptacross

Heptacross

A heptacross, is a regular 7-polytope with 14 vertices, 84 edges, 280 triangle faces, 560 octahedron cells, 672 5-cells "4-faces", 448 "5-faces", and 128 "6-faces".

It is a part of an infinite family of polytopes, called cross-polytopes or "orthoplexes". The dual polytope is the 7-hypercube, or hepteract.

The name "heptacross" is derived from combining the family name "cross polytope" with "hept" for seven (dimensions) in Greek.

Construction

There are two Coxeter groups associated with the "heptacross", one regular, dual of the hepteract with the C7 or [4,3,3,3,3,3] symmetry group, and a lower symmetry with two copies of 6-simplex facets, alternating, with the D7 or [34,1,1] symmetry group.

Cartesian coordinates

Cartesian coordinates for the vertices of a heptacross, centered at the origin are: (±1,0,0,0,0,0,0), (0,±1,0,0,0,0,0), (0,0,±1,0,0,0,0), (0,0,0,±1,0,0,0), (0,0,0,0,±1,0,0), (0,0,0,0,0,±1,0), (0,0,0,0,0,0,±1)

Every vertex pair is connected by an edge, except opposites.

See also

* Other 7-polytopes:
** 7-simplex - {36}
** 7-cube (hepteract) - {4,35}
** 7-demicube (demihepteract) - {31,4,1}
** 321 polytope - {33,2,1}
** 231 polytope - {32,3,1}
** 132 polytope - {31,3,2}
* Others in the cross-polytope family
** Octahedron - {3,4}
** Hexadecachoron - {3,3,4}
** Pentacross - {33,4}
** Hexacross - {34,4}
** Heptacross - {35,4}
** Octacross - {36,4}
** Enneacross - {37,4}
** Decacross - {38,4}

External links

*GlossaryForHyperspace | anchor=Cross | title=Cross polytope
* [http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
* [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Cross-polytope — In geometry, a cross polytope,[1] orthoplex,[2] hyperoctahedron, or cocube is a regular, convex polytope that exists in any number of dimensions. The vertices of a cross polytope are all the permutations of (±1, 0, 0, …, 0). The cross polytope is …   Wikipedia

  • List of mathematics articles (H) — NOTOC H H cobordism H derivative H index H infinity methods in control theory H relation H space H theorem H tree Haag s theorem Haagerup property Haaland equation Haar measure Haar wavelet Haboush s theorem Hackenbush Hadamard code Hadamard… …   Wikipedia

  • Pentacross — In five dimensional geometry, a pentacross, also called a triacontakaiditeron, is a five dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 octahedron cells, 32 5 cell hypercells.It is a part of an infinite family of polytopes …   Wikipedia

  • Hexacross — A hexacross, is a regular 6 polytope with 12 vertices, 60 edges, 160 triangle faces, 240 octahedron cells, 192 5 cell 4 faces , and 64 5 faces .It is a part of an infinite family of polytopes, called cross polytopes or orthoplexes . The dual… …   Wikipedia

  • Hepteract — A hepteract is a seven dimensional hypercube with 128 vertices, 448 edges, 672 square faces, 560 cubic cells, 280 tesseract 4 faces, 84 penteract 5 faces, and 14 hexeract 6 faces.The name hepteract is derived from combining the name tesseract… …   Wikipedia

  • Octaexon — An octexon, or octa 7 tope is a 7 simplex, a self dual regular 7 polytope with 8 vertices, 28 edges, 56 triangle faces, 70 tetrahedral cells, 56 5 cell 5 faces, 28 5 simplex 6 faces, and 8 6 simplex 7 faces.The name octaexon is derived from octa… …   Wikipedia

  • Octacross — An octacross, is a regular 8 polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 octahedron cells, 1792 5 cells 4 faces , 1792 5 faces , 1024 6 faces , and 256 7 faces .It is a part of an infinite family of polytopes, called cross… …   Wikipedia

  • Enneacross — An enneacross, is a regular 9 polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 octahedron cells, 4032 5 cells 4 faces , 5376 5 faces , 4608 6 faces , 2304 7 faces , and 512 8 faces .It is one of an infinite family of polytopes,… …   Wikipedia

  • Demihepteractic honeycomb — The demihepteractic heptacomb is a uniform space filling tessellation (or honeycomb) in Euclidean 7 space. It is constructed as an alternation of the regular hepteractic heptacomb.It is composed of two different types of facets. The hepteracts… …   Wikipedia

  • Decacross — A decacross, is a regular 10 polytope with 20 vertices, 180 edges, 960 triangle faces, 3360 octahedron cells, 8064 5 cells 4 faces , 13440 5 faces , 15360 6 faces , 11520 7 faces , 5120 8 faces , and 1024 9 faces .It is one of an infinite family… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”