User:Double sharp/Regiments

From [1]. Will be tidied up later.

0D, 1D, 2D

Monad and dyad have 1 member. Every polygon, star or convex, is a lone operative (one-membered regiment). Monad has a null verf, dyad has a monad verf, and the polygons have dyad verfs.

3D

Tettic

Tet = oox = oo's = s s s (equit, 4) – 1
Tut = oxx (isot, 12) – 1

Cubic

Cube = oo'x = o'x x = x x x (equit, 8) – 1
Oct = xo'o = oxo = ss s (square, 6) – 2 (thah)
Co = ox'o = xox (rectangle, 12) – 3 (oho, cho)
Tic = ox'x (isot, 24) – 1
Toe = xx'o = xxx (isot, 24) – 1
Sirco = xo'x (trapezoid, 24) – 3 (socco, sroh)
Girco = xx'x (scalene, 48) – 1
Snic = ss's (isosceles pentagon, 24) – 1
Quith = ox"x (isot, 24) – 1
Quitco = xx”x (scalene, 48) – 1
Gocco = (o'x"x) = (xo'x") = (ox"x') (trapezoid, 24) – 3 (querco, groh)
Cotco = (x'x"x) = (xx'x") = (xx"x') (scalene, 48) – 1

Doic

Doe = oo^x (equit, 20) – 1
Ike = xo^o = sss = ss'o (pentagon, 12)– 2 (gad)
Sissid = o^o*x (pentagon, 12) – 2 (gike)
Gissid = oo*x (equit, 20) – 1
Id = ox^o (rectangle, 30) – 3 (sidhid, seihid)
Did = o*x^o (rectangle, 30) – 3 (sidhei, gidhei)
Gid = o*xo (rectangle, 30) – 3 (gidhid, geihid)
Sidtid = (oo*x) = (o*xo) (ditrigon, 20) – 3 (ditdid, gidtid)
Tid = ox^x (isot, 60) – 1
Ti = xx^o (isot, 60) – 1
Tigid = o*x^x (isot, 60) – 1
Tiggy = o*xx (isot, 60) – 1
Quit Sissid = x*'x^o (isot, 60) – 1
Quit Gissid = x*'xo (isot, 60) – 1
Srid = xo^x (trapezoid, 60) – 3 (saddid, sird)
Raded = x*o^x (trapezoid, 60) – 3 (ided, ri)
Gidditdid = (o^x*'x) = (xo^x*') = (ox*'x^) (trapezoid, 60) – 3 (giid, giddy)
Gaddid = (o*x*'x) = (xo*x*') = (ox*'x*) (trapezoid, 60) – 3 (qrid, giddy)
Siid = (o*xx) = (xo*x) (trapezoid, 60) – 3 (sidditdid, siddy)
Grid = xx^x (scalene, 120) – 1
Quitdid = x*'x^x (scalene, 120) – 1
Gaquatid = x*'xx (scalene, 120) – 1
Idtid = (x^x*'x) (scalene, 120) – 1
Snid = ss^s (isosceles pentagon, 60) – 1
Siddid = s*s^s (irregular pentagon, 60) – 1
Gosid = s*ss (isosceles pentagon, 60) – 1
Isdid = s*'s^s (irregular fish, 60) – 1
Gisid = s*'ss (fish, 60) – 1
Girsid = s*'s,s (isosceles star, 60) – 1
Sided = (s^s*'s) (irregular fish, 60) – 1
Gisdid = (s*s*'s) (irregular fish, 60) – 1
Seside = (s*ss) = ss^o (isosceles ditrigon, 60) – 1
Sirsid = (s*'s,s) (star with pedestal, 60) – 1
Gidrid = [s*s,s*'s] ("isosceles hitch-hatched octagon", 60) – 1

Prisms

All have 1 member

4D

Pennic

Pen = ooox (tet, 5) – 1
Tip = ooxx (tripyr, 20) – 1
Rap = ooxo (trip, 10) – 3 (firp, pinnip)
Deca = oxxo (sphenoid, 30) – 1
Srip = oxox (wedge, 30) – 7 (rawvtip, sirdop, pirpop, garpop, pippindip, pinnipdip)
Grip = oxxx (scalenoid, 60) – 1
Gippid = xxxx (twisted disphenoid, 120) – 1
Spid = xoox (trap, 20) – 5 (piphid, duhd, phud, nipdip)
Prip = xoxx (trapyr, 60) – 3 (pittip, ripdip)

Tessic and related

Tes = ooo'x = oo'x x = o'x o'x = o'x x x = x x x x (tet, 16) – 1
Hex = xoo'o = x8o = o6o = ooo's = s s s s (oct, 8) – 2 (tho)
Ico = oxo'o = oo'ox = o9o (cube, 24) – 14 (ihi, oh, shahoh, hohoh, huhoh, ghahoh, ohuhoh, ratho, odho, hodho, hoh honho, dod honho, doh honho)
Rit = oox'o = x8x = o6x (trip, 32) – 5 (firt, hinnit, sto, gotto)
Tat = oox'x (trapyr, 64) – 1
Thex = xxo'o = x9o = o$o (squapyr, 48) – 2 (titho)
Srit = oxo'x (wedge, 96) – 7 (rawvatoth, sirdo, spript, garpit, pattinoth, pinpith)
Rico = xox'o = oo'xo = x6x (trip, 96) – 7 (rawvhitto, sirth, frico, gardoh, ini, hinpith)
Tah = oxx'o = x9x = o$x (disphenoid, 96) – 1
Grit = oxx'x (scalenoid, 192) – 1
Tico = xxx'o = oo'xx = x$x (trapyr, 192) – 1
Gidpith = xxx'x (irregular tet, 384) – 1
Sidpith = xoo'x (triangular antipodium, 64) – 8 (stefacoth, shafipto, steth, dippit, snappoth, snipto, iquipadah)
Ondip = ??? (blend of two sidpith verfs, 128) – 2 (sidtindip)
Prit = xxo'x (trapyr, 192) – 3 (sichado, sirpdo)
Proh = xox'x (trapyr, 192) – 3 (siphado, sirpith)
Sadi = sss'o = oo'ss = sSs (teddi, 96) – 1
Quitit = oox"x (trapyr, 64) – 1
Wavitoth = (o'x"x)o (wedge, 96) – 7 (qrit, girdo, gapript, gaqript, dippanoth, pinnatoth)
Gaqrit = oxx"x (scalenoid, 192) – 1
Thatoth = o(x'x"x) (scalenoid, 192) – 1
Thaquitoth = (x'x"x)o (scalenoid, 192) – 1
Gittith = o(o'x"x) (trigon podium, 64) – 8 (quidpith, picnut, gittifcoth, gahfipto, gnappoth, gnipto, gaquipadah)
Gondip = ??? (blend of two gittith verfs, 128) – 2 (gidtindip)
Gaquidpoth = xxx"x (irregular tet, 384) – 1
Thatpath = x(x'x"x) (irregular tet, 384) – 1
Thaquitpath = (x'x"x)x (irregular tet, 384) – 1
Quiproh = xox"x (trapyr, 192) – 3 (giphado, girpith)
Gichado = (o'x"x)x (trapyr, 192) – 3 (paqrit, girpdo)
Skiviphado = x(o'x"x) (skewed wedge, 192) – 15 (kavahto, gikviphado, kaviphdit, sik vipatoth, kavadipdit, sik vapippith, kavitpo, gik vapippith, kaviptit, gik vipatoth, sik vadiphto, kavatiphado, gik vadiphto, kevdiphato)
Rasdi = sss"o = oo"s,s (dual of teddi, 96) – 1
Rappisdi = (s'oo"s,) (trigonal faceting of sidtid, 96) – 3 (sirhapsippady, girhapsippady)

Icoic

Srico = ox'ox (wedge, 288) – 7 (rawvaty, sirdi, spirdy, gardi, dindi, inipdi)
Cont = ox'xo (sphenoid, 288) – 1
Grico = ox'xx (scalenoid, 576) – 1
Gippic = xx'xx (twisted disphenoid, 1152) – 1
Spic = xo'ox (squap, 144) – 20 (siddic, sripic, smiffadic, offadic, sandic, lifpic, sirc, ipi, inpac, picni, ridi, irnic, dipdi, sarnipadi, dirpidic, pifficdi, dinpi, dinic, inpic)
Prico = xo'xx (trapyr, 576) – 3 (sipti, sirpdi)
Wavaty = o(x'ox") (wedge, 288) – 7 (qrico, girdi, gapirdy, gaquerdy, pindi, inti)
Gic = ox"xo (sphenoid, 288) – 1
Gaqri = ox"xx (scalenoid, 576) – 1
Iquatoc = o(x'xx") (scalenoid, 576) – 1
Giddic = (ox"xo') (squap, 144) – 20 (quippic, gripic, gamfaddic, ofpic, gandic, lifdic, girc, idi, inic, dapni, ripi, irnpac, pic, garnipadi, dirpicdi, ifpic, ipindi, pinic, incdi)
Gaquapac = xx"xx (twisted disphenoid, 1152) – 1
Iquatpic = x(x'xx") (irregular tet, 1152) – 1
Doc = (xx"xx') (twisted disphenoid, 1152) – 1
Croc = (x'(x"x)'x) (twisted disphenoid, 1152) – 1
Coqroc = (x"(x'x)”x) (twisted disphenoid, 1152) – 1
Suti = (ox"xx') (trapyr, 576) – 3 (diquitdi, sirti)
Ditdi = (o'(x"x)'x) (trapyr, 576) – 3 (guti, girti)
Gipti = x(x'ox") (trapyr, 576) – 3 (paqri, girpdi)
Afdec = (o'(x"x)'o) (rectangular trapezoprism, 288) – 53 (girfaddic, ifdic, sirfaddic, rafdic, riftic, aftic, rafficdi, afti, rifti, afcuti, sirfpic, girfpic, afpaddic, gafpaddic, gafcappic, safcappic, sirfipdi, girfipdi, sirfpicti, girfpicti, sifpicti, gifpicti, safputi, gafputi, swifti, gwifti, snifti, gannifti, sif citi, gif citi, gifcuti, sifcuti, girfcuti, sirfcuti, girfopi, sirfopi, gifopi, sifopi, sirfipti, girfipti, girfupti, sirfupti, srifupti, grifupti, sifpacuti, gifpacuti, snifpacuti, gannifpacuti, sirfpacuti, girfpacuti, srifpacuti, grifpacuti)

Hyic

Hi = ooo^x (tet, 600) – 1
Ex = xoo^o (ike, 120) – 5 (fix, gohi, gahi, sisp)
Sishi = oo^o*x (doe, 120) – 22 (gaghi, sidtixhi, dittady, gidtixhi, idhi, paphicki, paphacki, ofiddady, gridixhi, didhi, sridixhi, sridaphi, gridaphi, dophi, radophi, sphix, spiddit, sispatit, gispatit, spittid, spaxhi)
Gishi = o^oo*x (ike, 120) – 5 (gashi, gofix, gax, gisp)
Gogishi = ooo*x (tet, 600) – 1
Thi = ooo^x (trippy, 2400) – 1
Tex = xxo^o (peppy, 1440) – 2 (tiffix)
Tighi = o^o*x^x (peppy, 1440) – 2 (taghi)
Tigaghi = oo*x^x (trippy, 2400) – 1
Tigfix = xx*o^o (peppy, 1440) – 2 (taggix)
Quit Sishi = oo^x*'x (trippy, 2400) – 1
Quit Gishi = o^ox*'x (peppy, 1440) – 2 (quit gashi)
Quit Gogishi = oox*'x (trippy, 2400) – 1
Tissidtixhi = (oo*x)x (ditrigon pyr, 2400) – 3 (tidtidohi, tiggidtixhi)
Rahi = oox^o (trip, 1200) – 3 (fry, shinhi)
Rasishi = oo^x*o (trip, 1200) – 3 (firsashi, hinhi)
Ragaghi = oo*x^o (trip, 1200) – 3 (firgaghi, mohiny)
Rigogishi = oox*o (trip, 1200) – 3 (firgogishi, gohiny)
Rox = oxo^o (pip, 720) – 15 (rofix, sophi, sprapivady, frox, rixhi, sriphi, ipixady, lifpipixhi, nipixady, som fapathi, sofapathi, sniffipathi, paphiny, sirphinady)
Righi = o^o*x^o (pip, 720) – 15 (raghi, papvixhi, giprapivady, froghi, ridhei, mriphi, sipathi, lifpixady, snipathi, mom fapathi, gofapathi, mim fipathi, pixhiny, girphinady)
Ragishi = o^ox*o (pip, 720) – 15 (ragashi, spapivady, prap vixhi, frogshi, rihix, griphi, mipathi, sliffipathi, minnipathi, gom fapathi, ofapaxady, gam fipathi, spidhiny, irp xanady)
Rigfix = o^ox*o (pip, 720) – 15 (raggix, gippapivady, quiphi, frogfix, ripahi, graphi, gipathi, gliffipathi, ganipathi, omfapaxady, ofpipixhi, mif pixady, gipdohiny, irp panady)
Srahi = oxo^x (wedge, 3600) – 7 (srawvixady, sirdhi, spriphi, garphi, phinxhi, pinpixhi)
Srix = xox^o (wedge, 3600) – 7 (srawv hixhi, rassixhi, pirsady, garsixhi, sid hinxhi, hinpixhi)
Sirfix = xo^x*o (wedge, 3600) – 7 (srawvathi, rashihy, sprahihy, garady, sid hinady, hinipady)
Sirsashi = ox^o*x (wedge, 3600) – 7 (mrawv hixhi, rashix, pirsixhi, garsady, sixhinady, shinipady)

... (there are a lot more)

Special antiprisms

Gap = [[s^s] [s^s]] (dissected ike, 100) – 1
Gudap = s^s s*'s (star gyrobifastigium with one wedge crossed and one uncrossed, 50) – 1
Padiap = [[s*'s] [s*'s]] (dissected gike, 100) – 1
Sidtidap = (oo*x) s (tricu, 40) – 3 (ditdidap, gidtidap)

Prismatic

These follow the 3D regiments.

Duoprisms

All have 1 member

Antiduoprisms

All have 1 member

5D

Hixic

Pentic

Hinnic

Hin = oo8x = oo6o (rap, 16) – 6 (dah, han, radah, rinah, hit)
Thin = oo9x = oo$o (trippyr, 160) – 3 (tadah, tohan)
Sirhin = ox8x = ox6o (trigon fastegium, 160) – 37 (...)
Siphin = xo8x = xo6x (tet-oct cupola, 80) – 56 (...)
Girhin = ox9x = ox$o (disphenoidpyr, 480) – 1
Giphin = xx9x = xx$o (irtetoid, 960) – 1
Pithin = xo9x = xo$x (wedgepyr, 480) – 7 (...)
Pirhin = xx8x = xx6o (skewed trippyr, 320) – 7 (...)

Miscellaneous

Sidtaxhiap = ooo^s s (tet-tut cupola, 1200) – 1
Gadtaxhiap = ooo*'s s (tet-tetrapod cupola, 1200) – 1

6D

Hoppic

Hop = ooooox (hix, 7) – 1
Ril = ooooxo (pen prism, 21) – 7
Bril = oooxoo (trigon-tet duoprism, 35) – 18
Til = ooooxx (pen pyramid, 42) – 1
Batal = oooxxo (tet-dyad disphenoid, 105) – 1
Fe = ooxxoo (trigon disphenoid, 140) – 1
Sril = oooxox (tet prism wedge, 105) – 31
Spil = ooxoox (triddip antifastegium, 140) – 138
Sabril = ooxoxo (trigon-dyad duowedge, 210) – 63
Scal = oxooox (tet antifastegium, 105) – 132
Sibpof = oxooxo (trigon duoantifastegium, 210) – 143
Staf = xoooox (pen antiprism, 42) – 19
Gril = oooxxx (tet scalenoid, 210) – 1
Gapil = ooxxxx (trigon irtetoid, 840 – 1
Gabril = ooxxxo (trigon-dyad disphenoid pyr, 420) – 1
Gacal = oxxxxx (irpenoid, 2520) – 1
Gibpof = oxxxxo (disphenoid scalenoid, 1260) – 1
Gotaf = xxxxxx (irregular hix, 5040) – 1
Patal = ooxoxx (trip wedge pyr, 420) – 15
Pril = ooxxox (trigon-rectangle disphenoid, 420) – 3 (rapril, lapril)
Bapril = oxoxxo (wedge-dyad disphenoid, 630) – 7
Catal = oxooxx (trigon antifastegium, 420) – 37
Cral = oxoxox ((square-dyad disphenoid)-square wedge, 630) – 75
Copal = oxxoox (trap-dyad disphenoid, 420) – 7
Tocal = xoooxx (tet antiprism pyr, 210) – 15
Topal = xooxox (trip-antifastegium wedge, 420) – 139
Cagral = oxoxxx (wedge pyrpyr, 1260) – 7
Captal = oxxoxx (trapezoid-dyad disphenoid pyr, 1260) – 3 (recaptal, lacaptal)
Copril = oxxxox (trapezoid-dyad disphenoid pyr, 1260) – 3 (recopril, lacopril)
Togral = xooxxx (trappyrpyr, 840) – 7
Tactaf = xxooxx (trappyrpyr, 840) – 5
Tocral = xoxoxx (square-sphenoid wedge pyr, 1260) – 27
Taporf = xoxxox (rectangle disphenoid, 1260) – 6 (ratparl, latparl, ratporf, latporf, raltporlil)
Tagopal = xoxxxx (rectanglepyrpyrpyr, 2520) – 3 (ratgopal, latgopal)
Tacogral = xxoxxx (rectanglepyrpyrpyr, 2520) – 3 (ratcogral, latcogral)

Axic

Haxic

Jakic

Miscellaneous

Ontip = ??? (blend of two stoxog verfs, 1536) – ??
Gontip = ??? (blend of two goxaxog verfs, 1536) – ??

7D

...

8D

...