Polytopes of Various Dimensions


This page contains a list of names for n-D polytopes, such as polyhedron for 3-D. The names polygon and polyhedron were known for a long time. Polychoron was coined by Norman Johnson by shortening George Olshevsky's polychorema. Later George and I coined names such as polytetron, polypenton, and polyhexon - however these names had a problem - for example is a hecatonicosatetron a 120 sided polytetron (5-D) or a 100 sided icosatetron (25-D) - because of this Wendy Kreiger came up with a way to avoid this confusion by calling the 5-D polytope a polyteron - she coined the names for 5-D up to 9-D by using the prefixes used in the metric system - tera, peta, exa, zetta, and yotto - these prefixes are actually a shortened or modified form of the Greek prefixes tetra, penta, hexa, hepta, and octa. I later extended this process to go up to a tridecillion dimensions - my name for a 25-D polytope is a polyicteron - where ic is short for icosi and tera is short for tetra. Also notice that the suffixes are for one less than the dimension - ie 5-D is polyteron where tera is short for tetra = 4 - this is because a polyteron has many terons (4-D elements), not many petons (5-D elements) - however a polyteron can be a peton of a polypeton (6-D). To get the plural of the polytope (for dimensions 3 and up), change on to a - for example the plural of polyictron is polyictra, for dimensions 2 and down just add an s. The plurals to polytope elements are found by adding an s - i.e. the plurals for teron and ictron are terons and ictrons. So now for the list:

Null polytope - -1 dimensions, sometimes called "the essence" of a polytope.

Monad - 0 dimensions, shows up as vertices of other polytopes.

Polytelon - 1 dimension - only uniform member is the ditelon which is also called ditel and dyad - or just plain line segment - found as edges.

Polygon - 2 dimensions - examples are triangle, square, and pentagon - found as faces.

Polyhedron - 3 dimensions - examples are tet, oct, and gaquatid - found as cells of higher polytopes.

Polychoron - 4 dimensions - found as terons.

Polyteron - 5 dimensions - first called polytetron.

Polypeton - 6 dimensions - first called polypenton - one of my favorites is the Gosset polypeton with 27 vertices which I call Jak.

Polyecton - 7 dimensions - first called polyhexon and then polyexon.

Polyzetton - 8 dimensions - the most famous one is Fy - it is the Gosset polytope with 240 vertices.

Polyyotton - 9 dimensions - this dimension has interesting powertopes.

Polyxennon - 10 dimensions - xenna being a play on ennea (which means 9).

Polydakon - 11 dimensions.

Polyhendon - 12 dimensions - henda being a shortened form of hendeca.

Polydokon - 13 dimensions - it's amazing how little we hear of 13 dimensional shapes - so here's an example - the tetradecadokon - the 13-simplex.

Polytradakon - 14 dimensions.

Polytedakon - 15 dimensions - once called polyteradakon.

Polypedakon - 16 dimensions - once called polypetadakon.

Polyexdakon - 17 dimensions.

Polyzedakon - 18 dimensions.

Polyyodakon - 19 dimensions.

Polynedakon - 20 dimensions - once called polyxendakon

Polyicon - 21 dimensions. - pronounced (POL ee I con), not (poll YIC un).

Polyikenon - 22 dimensions.

Polyicodon - 23 dimensions.

Polyictron - 24 dimensions - the Leech polytope is a famous polyictron - which I suspect may be scaliform.

Polyicteron - 25 dimensions - fun powertopes here!

Polyicpeton - 26 dimensions.

Polyikecton - 27 dimensions.

Polyiczeton - 28 dimensions - once called polyiczetton.

Polyikyoton - 29 dimensions - once called polyikyotton.

Polyicxenon - 30 dimensions - once called polyicxennon.

Polytracon - 31 dimensions, change tracon to trakenon, tracodon, tractron, tracteron, tracpeton, trakecton, traczeton, trakyoton, and tracxenon - to go from 32 to 40 dimensions.

Polytecon - 41 dimensions, like above - change the "tra" to "te" - for example if you went to the 45th dimension, you could hold a uniform polytecteron. - once called polyteracon.

Polypecon - 51 dimensions. - originally called polypetacon.

Polyexacon - 61 dimensions - pronounced (POL ee EX a con). - for the Metal Gear Solid fans out there "I need scissors, polyexacon" - I just had to say that :)

Polyzacon - 71 dimensions.

Polyyocon - 81 dimensions - nightmare homework assignment - list all of the uniform polyyoca!!

Polynecon - 91 dimensions.

Polynecxenon - 100 dimensions - once called polyxencxennon.

Polyhoton - 101 dimensions - hota is a play on hecaton.

Polyhotenon - 102 dimensions - continue with hotodon, hotron, hoteron, hopeton, hotecton, hozeton, hoyoton, and hoxenon to get to 110 dimensions.

Polyhodakon - 111 dimensions - continue with hotendon, hodokon, hotradakon, hotedakon, hopedakon, hotexdakon, hozedakon, hoyodakon, honedakon to get to 120 dimensions.

Polyhoticon - 121 dimensions.

Polyhotracon - 131 dimensions - continue with polyhotecon (141-D), polyhopecon (151-D), polyhotexacon (161), polyhozacon (171), polyhoyocon (181), and polyhonecon (191).

Polydoton - 201 dimensions - guess what polydozedakon means? - answer 218 dimensional polytope.

Polytroton - 301 dimensions.

Polytoton - 401 dimensions - once called polyteroton.

Polypoton - 501 dimensions - once called polypetoton.

Polyexoton - 601 dimensions.

Polyzoton - 701 dimensions.

Polyyooton - 801 dimensions.

Polynoton - 901 dimensions - once called polyxenoton.

Polynonecxenon - 1000 dimensions. - Also the name for a xenon breathing parrot which has no neck - NOT!

Polykalon - 1001 dimensions - once called polykillon.

Polykalenon - 1002 dimensions - continue with kalodon, kaltron, kalteron, kalpeton, kalecton, kalzeton, kalyoton, kalxenon (1010), keep on going with kaldakon, kalhendon, kaldokon, kaltradakon, kaltedakon, kalpedakon, kalexdakon, kalzedakon, kalyodakon, kalnedakon (1020).

Polykalicon - 1021 dimensions - continue with kaltracon (1031), kaltecon (1041), kalpecon (1051), kalexacon (1061), kalzacon (1071), kalyocon (1081), and kalnecon (1091).

Polykalhoton - 1101 dimensions - continue with kaldoton (1201), kaltroton (1301), kaltoton (1401), kalpoton (1501), kalexoton (1601), kalzoton (1701), kalyooton (1801), and kalnoton (1901).

Polydalon - 2001 dimensions - a 2006 dimensional polytope would be a polydalpeton.

Polytralon - 3001 dimensions.

Polytalon - 4001 dimensions - continue with palon (5001), exalon (6001), zalon (7001), yalon (8001), and nalon (9001).

Polydakalon - 10,001 dimensions - continue with hendalon, dokalon, tradakalon, tedakalon, pedakalon, exdakalon, zedakalon, yodakalon, and nedakalon - each 1000 dimensions apart - so a polynedakalon is 19,001 dimensional.

Polyicalon - 20,001 dimensions - continue with ikenalon, icodalon, ictralon, ictalon, icpalon, ikexalon, iczalon, ikyalon, and icnalon - 1000 dimensions apart.

Polytrakalon - 30,001 dimensions.

Polytecalon - 40,001 dimensions - continue with pecalon, exacalon, zacalon, yokalon, and necalon - 10,000 dimensions apart.

Polyhotalon - 100,001 dimensions.

Polymejon - 1,000,001 dimensions - once called polymegon - but the -gon ending can be confusing - continue with dejon, trejon, tejon, pejon, exejon, zejon, yejon, and nejon - 1 million dimensions apart.

Polydakejon - 10,000,001 dimensions - continue with ikejon, trakejon, tekejon, pekejon, exakejon, zakejon, yokejon, and nakejon - 10 million dimensions apart.

Polyhotejon - 100,000,001 dimensions.

Polygijon - 1,000,000,001 dimensions - once called polygigon - but changed due to the -gon ending - continue with dijon, trijon, tijon, pijon, exijon, zijon, yijon, and nijon - 1 billion dimensions apart.

Polydakijon - 10,000,000,001 dimensions

Polyhotijon - 100,000,000,001 dimensions.

Polyaston - 1 trillion 1 dimension - asti short for asteroid - which probably weighs about a trillion kilotons.

Polylunon - 1 quadrillion 1 dimensions - luni comes from lunar.

Polyfirmon - 1 quintillion 1 dimensions - firmi comes from terra firma - or Earth.

Polyjovon - 1 sextillion 1 dimensions - jovi represents Jupiter.

Polysolon - 1 septillion 1 dimensions - soli represents Sol - the sun.

Polybeton - 1 octillion 1 dimensions - bet short for Betelgeuse.

Polyglocon - 1 nonillion 1 dimensions - gloc short for globular cluster.

Polygaxon - 1 decillion 1 dimensions - gax short for galaxy - Not to be confused with the polychoron gax.

Polysupon - 1 undecillion 1 dimensions - sup for super cluster. - Just coined this one and the two below.

Polyverson - 1 dodecillion 1 dimensions - vers for universe.

Polymulton - 1 tridecillion 1 dimensions - multi for multiverse.


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