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A pentachoron is a 4-dimensional simplex. It is also called the pyrochoron under the elemental naming scheme. Its Bowers acronym is "pen".

Properties Edit


The pentachoron is the pyramid on the tetrahedron, with 4 tetrahedra on each vertex.

Hypervolumes Edit

  • vertex count = 5
  • edge length = 10l
  • surface area = \frac { 5\sqrt { 3 }  }{ 2 } { l }^{ 2 }
  • surcell volume = \frac { \sqrt { 2 }  }{ 3 } { l }^{ 3 }
  • surteron bulk = \frac { \sqrt { 5 }  }{ 96 } { l }^{ 4 }

Subfacets Edit

See also Edit

Zeroth First Second Third Fourth Fifth Sixth Seventh Eighth Ninth Tenth Eleventh Twelfth Thirteenth Fourteenth Fifteenth Sixteenth
Simplex Point Line Triangle Tetrahedron Pentachoron Hexateron Heptapeton Octaexon Enneazetton Decayotton Hendecaxennon Dodecadakon Tredecahendakon Quattuordecadokon Quindecatradakon Sexdecateradakon Septendecapetadakon
Hypercube Point Line Square Cube Tesseract Penteract Hexeract Hepteract Octeract Enneract Dekeract Undekeract Dodekeract Tredekeract Quattuordekeract Quindekeract Sexdekeract
Cross Point Line Square Octahedron Tetrarss Pentarss Hexarss Heptarss Octarss Ennearss Decarss Hendecarss Dodecarss Tredecarss Quattuordecarss Quindecatrarss Sexdecaterarss
Hypersphere Point Line Circle Sphere Glome Hyperglome Hexaphere Heptaphere Octaphere Enneaphere Decaphere Hendecaphere Dodecaphere Tredecaphere Quattuordecaphere Quindecatraphere Sexdecateraphere

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