different between octachoron vs tesseract

English

Etymology

octa- (“eight”) +? -choron (“room”), from Ancient Greek ????- (oktá-, “eight”) and ????? (kh?ros, “room”).

Noun

octachoron (plural octachorons or octachora)

1. (mathematics) A four-dimensional object equivalent to a cube, constructed out of eight cubes.
   • 2012, Yequn Zhang, Murat Arabaci, and Ivan B. Djordjevic, Rate-Adaptive Four-Dimensional Nonbinary LDPC-Coded Modulation for Long-Haul Optical Transport Networks, page 3:

     Our 16-point 4D constellation is described by the set {(±1,±1,±1,±1)}, which is indeed the set of vertices of a tesseract (i.e., a regular octachoron) [4].

   • 2013, Milorad Cvijetic and Ivan B. Djordjevic, Advanced Optical Communication Systems and Networks, page 357:

     The Schlegel diagram from this figure is a projection of a regular octachoron from the 4-D space to the 3-D space through a point beyond one of its facets.

   • 2013, Paul Jennings and Frank Nijhoff, On an elliptic extension of the Kadomtsev-Petviashvili equation, page 4:

     ...completing the notation for the vertices of an elementary lattice octachoron.

Synonyms

• 4-cube
• 8-cell
• hypercube
• tesseract

Translations

English

Etymology

From tessara- (“four-”) +? Ancient Greek ????? (aktís, “ray”).

Noun

tesseract (plural tesseracts)

1. (mathematics) The four-dimensional analogue of a cube; a 4D polytope bounded by eight cubes (in the same way a cube is bounded by six squares).
2. (science fiction) Any of various fictional mechanisms that explain extradimensional, superluminal, or time travel outside the geometry of the physical universe.

Synonyms

• (analogue of a cube): four-dimensional hypercube, 4-cube, 8-cell, octachoron, tetracube

Hypernyms

• hypercube, polytope

Derived terms

• tesseractic

Translations

See also

• tesseract on Wikipedia.Wikipedia
• Mathworld article on the tesseract

Anagrams

• rascettes