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.
