User blog:Cheetahrock63/Extended polytope names

got bored so i made possibly my most useless post in a while

so i took to naming types of polytope. some of them with big enough infinite dimensionalities that they can't be proven to exist in ZFC. neato. because who wouldn't want to take the Cartesian product of inaccessible cardinal-ly many line segments to get a hypercube with inaccessible cardinal-ly many dimensions?

trillion+1 to tredecillion+1 (the ones in bold) are Bowers' names. everything after is mein

the eponymously named -illion of some a name below referring to a polytope of finite dimensionality $n$ (e.g. Polyaston to Astillion) is equal to $10^{3+ 3 \cdot 10^{3\cdot 10^{3 \cdot (n - 1)}}}$. So a "gigavillion" would be equal to $10^{3+ 3 \cdot 10^{3\cdot 10^{3 \cdot 10^{48}}}}$.

also "$\rm {Card}$" is defined to be the "cardinality" (second cardinality?) of ${\rm {Ord}}$. $2^{\rm {Card}}$ is the "cardinality" of the powerconglomerate of ${\rm {Ord}}$. both "cardinalities" can be shown to exist in ACG because of course they can.

keep in mind that the only regular polytopes of such high finite dimensionalities comprise of literally just the really high-dimensional simplex, the high-dimensional hypercube, and the hypercube's dual—the high-dimensional cross polytope.

now uniform on the other hand...

Dimensionality	Polytope name	Eponym
1 trillion and 1	Polyaston	Asteroids
1 quadrillion and 1	Polylunon	The Moon (luna)
1 quintillion and 1	Polyfirmon	Earth (terra firma)
1 sextillion and 1	Polyjovon	Jupiter (Jove)
1 septillion and 1	Polysolon	The Sun (sol)
1 octillion and 1	Polybeton	Betelgeuse
1 nonillion and 1	Polyglocon	Globular clusters
1 decillion and 1	Polygaxon	Galaxy
1 undecillion and 1	Polysupon	Supercluster
1 duodecillion and 1	Polyverson	Universe
1 tredecillion and 1	Polymulton	Multiverse
1 quattordecillion and 1	Polymegavon	Megaverse
1 quindecillion and 1	Polygigavon	Gigaverse
1 sexdecillion and 1	Polyteravon	Teraverse
1 septendecilllion and 1	Polypetavon	Petaverse
1 octodecillion and 1	Polyexavon	Exaverse
1 novemdecillion and 1	Polyzettavon	Zettaverse
1 vigintillion and 1	Polyxennavon	Xennaverse
1 unvigintillion and 1	Polywekavon	Wekaverse
1 duovigintillion and 1	Polyvendekavon	Vendekaverse
1 trevigintillion and 1	Polyudekavon	Udekaverse
1 quattorvigintillion and 1	Polytredavon	Tredaverse
1 quinvigintillion and 1	Polysortavon	Sortaverse
1 sexvigintillion and 1	Polyrintavon	Rintaverse
1 septenvigintillion and 1	Polyquexavon	Quexaverse
1 octovigintillion and 1	Polypeptavon	Peptaverse
1 novemvigintillion and 1	Polyochavon	Ochaverse
1 trigintillion and 1	Polynenavon	Nenaverse
1 untrigintillion and 1	Polymingavon	Mingaverse
1 googol and 1	Polygogoron	Googol
1 duotrigintillion and 1	Polylumavon	Lumaverse
1 tretrigintillion and 1	Polykamavon	Kamaverse
1 quattortrigintillion and 1	Polyjameavon	Jameaverse
1 quintrigintillion and 1	Polyiamavon	Iamaverse
1 sextrigintillion and 1	Polyhevavon	Hevaverse
1 septentrigintillion and 1	Polygrinavon	Grinaverse
1 octotrigintillion and 1	Polyfremavon	Fremaverse
1 novemtrigintillion and 1	Polyechavon	Echaverse
1 quadragintillion and 1	Polydrunavon	Drunaverse
1 unquadragintillion and 1	Polyceravon	Ceraverse
1 duoquadragintillion and 1	Polybrutavon	Brutaverse
1 trequadragintillion and 1	Polyaritavon	Aritaverse
1 googolplex and 1	Polygogoplaron	Googolplex
Graham's number and 1	Polygraharon	Graham's number
TREE(3) and 1	Polyarbotrion	TREE(3) (arbor)
Rayo's number and 1	Polyrayoron	Rayo's number
$\aleph_0$	Polyomnon	Omniverse
$\aleph_1$	Polybarrelon / Polymonon	Barrel / Monocosm
Failed to parse (unknown function "\frak"): {\displaystyle \frak {c}}	Polycontinuon (same thing as a Polymonon if CH holds)	Continuum
$\alef_2$	Polybebon	Beyond bubble
$\aleph_3$	Polytranson	Transcendentem, "Polytracon" (31D polytopes) is taken
$\aleph _ 4$	Polytraconon	Transcendentem Continuum
$\alef_\omega$	Polysecon	Secode
$\aleph_{\varepsilon_0}$	Polyepsinicynon	$\varepsilon_0$Cynoverses
$\aleph_{\Gamma_0}$	Polyfescho-on	Feferman–Schütte ordinal
$\aleph_{\vartheta (\Omega^3)}$	Polyacko-on	Ackermann ordinal
$\aleph_{\vartheta (\Omega^\omega)}$	Polysvo-on	Small Veblen ordinal
$\aleph_{\vartheta (\Omega^\Omega)}$	Polylvo-on	Large Veblen ordinal
$\aleph_{\vartheta (\varepsilon_{\Omega+1})}$	Polybachowo-on	Bachmann-Howard ordinal
$\aleph_{\psi (\varepsilon_{\Omega_\omega+1})}$	Polytakefucho-on	Takeuti-Feferman-Buchholz ordinal
Failed to parse (unknown function "\frak"): {\displaystyle \aleph_{\omega_1^{\frak {Ch}}}}	Polyochesso-on	Omega one of chess
$\aleph_{\omega_1^{CK}}$	Polychukleon	Church-Kleene ordinal
$\aleph_{\omega_1}$	Polygomon	Great Omniverse
$\aleph_{\psi_I (0)}$	Polyafixon	Aleph fixed point
$I$	Polywinacon	Weakly Inaccessible cardinal
$\mathcal{I}$	Polysinacon (same thing as a polywinacon if GCH holds)	Strongly Inaccessible cardinal
$M$	Polywmahlocon	Weakly Mahlo cardinal
$\mathcal{M}$	Polysmahlocon (same thing as a polywmalocon if GCH holds)	Strongly Mahlo cardinal
$K$	Polywecompacon	Weakly compact cardinal
$\rm {Card}$	Polybomon / Polyordon / Polysoupon	Big Omniverse / ${\rm {Ord}}$ / Soupcount
$2^{\rm {Card}}$	Polyficonglomovon	First proper conglomoverse

and just for the fun of it

Dimensionality	Name	Eponym
CAI (the holo ξ one that just has all the collections. it's different and smaller than E_0 i think?)	Polybarrexon / Polycollecton	The Barrelplex / Collections
E_0	Polyselvon	Selfverses
∞_ALL	Polymaioron	Maiorverse
CAI (the serge one with the MPR)	Polyarcon	The Box (arca)

because who wouldn't want to consider a hypercube with all the dimensions—regardless of internal properties, they are all in it?

well, probably me since i'm pretty indifferent towards hypercosmology but maybe one of them hypercosmology nerds would be. key word is "maybe".