Polytope of Type {2,336}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,336}*1344
if this polytope has a name.
Group : SmallGroup(1344,5829)
Rank : 3
Schlafli Type : {2,336}
Number of vertices, edges, etc : 2, 336, 336
Order of s₀s₁s₂ : 336
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,168}*672
   3-fold quotients : {2,112}*448
   4-fold quotients : {2,84}*336
   6-fold quotients : {2,56}*224
   7-fold quotients : {2,48}*192
   8-fold quotients : {2,42}*168
   12-fold quotients : {2,28}*112
   14-fold quotients : {2,24}*96
   16-fold quotients : {2,21}*84
   21-fold quotients : {2,16}*64
   24-fold quotients : {2,14}*56
   28-fold quotients : {2,12}*48
   42-fold quotients : {2,8}*32
   48-fold quotients : {2,7}*28
   56-fold quotients : {2,6}*24
   84-fold quotients : {2,4}*16
   112-fold quotients : {2,3}*12
   168-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 10, 17)( 11, 23)( 12, 22)( 13, 21)( 14, 20)
( 15, 19)( 16, 18)( 25, 30)( 26, 29)( 27, 28)( 31, 38)( 32, 44)( 33, 43)
( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 45, 66)( 46, 72)( 47, 71)( 48, 70)
( 49, 69)( 50, 68)( 51, 67)( 52, 80)( 53, 86)( 54, 85)( 55, 84)( 56, 83)
( 57, 82)( 58, 81)( 59, 73)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)
( 65, 74)( 87,129)( 88,135)( 89,134)( 90,133)( 91,132)( 92,131)( 93,130)
( 94,143)( 95,149)( 96,148)( 97,147)( 98,146)( 99,145)(100,144)(101,136)
(102,142)(103,141)(104,140)(105,139)(106,138)(107,137)(108,150)(109,156)
(110,155)(111,154)(112,153)(113,152)(114,151)(115,164)(116,170)(117,169)
(118,168)(119,167)(120,166)(121,165)(122,157)(123,163)(124,162)(125,161)
(126,160)(127,159)(128,158)(171,255)(172,261)(173,260)(174,259)(175,258)
(176,257)(177,256)(178,269)(179,275)(180,274)(181,273)(182,272)(183,271)
(184,270)(185,262)(186,268)(187,267)(188,266)(189,265)(190,264)(191,263)
(192,276)(193,282)(194,281)(195,280)(196,279)(197,278)(198,277)(199,290)
(200,296)(201,295)(202,294)(203,293)(204,292)(205,291)(206,283)(207,289)
(208,288)(209,287)(210,286)(211,285)(212,284)(213,318)(214,324)(215,323)
(216,322)(217,321)(218,320)(219,319)(220,332)(221,338)(222,337)(223,336)
(224,335)(225,334)(226,333)(227,325)(228,331)(229,330)(230,329)(231,328)
(232,327)(233,326)(234,297)(235,303)(236,302)(237,301)(238,300)(239,299)
(240,298)(241,311)(242,317)(243,316)(244,315)(245,314)(246,313)(247,312)
(248,304)(249,310)(250,309)(251,308)(252,307)(253,306)(254,305);;
s2 := (  3,179)(  4,178)(  5,184)(  6,183)(  7,182)(  8,181)(  9,180)( 10,172)
( 11,171)( 12,177)( 13,176)( 14,175)( 15,174)( 16,173)( 17,186)( 18,185)
( 19,191)( 20,190)( 21,189)( 22,188)( 23,187)( 24,200)( 25,199)( 26,205)
( 27,204)( 28,203)( 29,202)( 30,201)( 31,193)( 32,192)( 33,198)( 34,197)
( 35,196)( 36,195)( 37,194)( 38,207)( 39,206)( 40,212)( 41,211)( 42,210)
( 43,209)( 44,208)( 45,242)( 46,241)( 47,247)( 48,246)( 49,245)( 50,244)
( 51,243)( 52,235)( 53,234)( 54,240)( 55,239)( 56,238)( 57,237)( 58,236)
( 59,249)( 60,248)( 61,254)( 62,253)( 63,252)( 64,251)( 65,250)( 66,221)
( 67,220)( 68,226)( 69,225)( 70,224)( 71,223)( 72,222)( 73,214)( 74,213)
( 75,219)( 76,218)( 77,217)( 78,216)( 79,215)( 80,228)( 81,227)( 82,233)
( 83,232)( 84,231)( 85,230)( 86,229)( 87,305)( 88,304)( 89,310)( 90,309)
( 91,308)( 92,307)( 93,306)( 94,298)( 95,297)( 96,303)( 97,302)( 98,301)
( 99,300)(100,299)(101,312)(102,311)(103,317)(104,316)(105,315)(106,314)
(107,313)(108,326)(109,325)(110,331)(111,330)(112,329)(113,328)(114,327)
(115,319)(116,318)(117,324)(118,323)(119,322)(120,321)(121,320)(122,333)
(123,332)(124,338)(125,337)(126,336)(127,335)(128,334)(129,263)(130,262)
(131,268)(132,267)(133,266)(134,265)(135,264)(136,256)(137,255)(138,261)
(139,260)(140,259)(141,258)(142,257)(143,270)(144,269)(145,275)(146,274)
(147,273)(148,272)(149,271)(150,284)(151,283)(152,289)(153,288)(154,287)
(155,286)(156,285)(157,277)(158,276)(159,282)(160,281)(161,280)(162,279)
(163,278)(164,291)(165,290)(166,296)(167,295)(168,294)(169,293)(170,292);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(338)!(1,2);
s1 := Sym(338)!(  4,  9)(  5,  8)(  6,  7)( 10, 17)( 11, 23)( 12, 22)( 13, 21)
( 14, 20)( 15, 19)( 16, 18)( 25, 30)( 26, 29)( 27, 28)( 31, 38)( 32, 44)
( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 45, 66)( 46, 72)( 47, 71)
( 48, 70)( 49, 69)( 50, 68)( 51, 67)( 52, 80)( 53, 86)( 54, 85)( 55, 84)
( 56, 83)( 57, 82)( 58, 81)( 59, 73)( 60, 79)( 61, 78)( 62, 77)( 63, 76)
( 64, 75)( 65, 74)( 87,129)( 88,135)( 89,134)( 90,133)( 91,132)( 92,131)
( 93,130)( 94,143)( 95,149)( 96,148)( 97,147)( 98,146)( 99,145)(100,144)
(101,136)(102,142)(103,141)(104,140)(105,139)(106,138)(107,137)(108,150)
(109,156)(110,155)(111,154)(112,153)(113,152)(114,151)(115,164)(116,170)
(117,169)(118,168)(119,167)(120,166)(121,165)(122,157)(123,163)(124,162)
(125,161)(126,160)(127,159)(128,158)(171,255)(172,261)(173,260)(174,259)
(175,258)(176,257)(177,256)(178,269)(179,275)(180,274)(181,273)(182,272)
(183,271)(184,270)(185,262)(186,268)(187,267)(188,266)(189,265)(190,264)
(191,263)(192,276)(193,282)(194,281)(195,280)(196,279)(197,278)(198,277)
(199,290)(200,296)(201,295)(202,294)(203,293)(204,292)(205,291)(206,283)
(207,289)(208,288)(209,287)(210,286)(211,285)(212,284)(213,318)(214,324)
(215,323)(216,322)(217,321)(218,320)(219,319)(220,332)(221,338)(222,337)
(223,336)(224,335)(225,334)(226,333)(227,325)(228,331)(229,330)(230,329)
(231,328)(232,327)(233,326)(234,297)(235,303)(236,302)(237,301)(238,300)
(239,299)(240,298)(241,311)(242,317)(243,316)(244,315)(245,314)(246,313)
(247,312)(248,304)(249,310)(250,309)(251,308)(252,307)(253,306)(254,305);
s2 := Sym(338)!(  3,179)(  4,178)(  5,184)(  6,183)(  7,182)(  8,181)(  9,180)
( 10,172)( 11,171)( 12,177)( 13,176)( 14,175)( 15,174)( 16,173)( 17,186)
( 18,185)( 19,191)( 20,190)( 21,189)( 22,188)( 23,187)( 24,200)( 25,199)
( 26,205)( 27,204)( 28,203)( 29,202)( 30,201)( 31,193)( 32,192)( 33,198)
( 34,197)( 35,196)( 36,195)( 37,194)( 38,207)( 39,206)( 40,212)( 41,211)
( 42,210)( 43,209)( 44,208)( 45,242)( 46,241)( 47,247)( 48,246)( 49,245)
( 50,244)( 51,243)( 52,235)( 53,234)( 54,240)( 55,239)( 56,238)( 57,237)
( 58,236)( 59,249)( 60,248)( 61,254)( 62,253)( 63,252)( 64,251)( 65,250)
( 66,221)( 67,220)( 68,226)( 69,225)( 70,224)( 71,223)( 72,222)( 73,214)
( 74,213)( 75,219)( 76,218)( 77,217)( 78,216)( 79,215)( 80,228)( 81,227)
( 82,233)( 83,232)( 84,231)( 85,230)( 86,229)( 87,305)( 88,304)( 89,310)
( 90,309)( 91,308)( 92,307)( 93,306)( 94,298)( 95,297)( 96,303)( 97,302)
( 98,301)( 99,300)(100,299)(101,312)(102,311)(103,317)(104,316)(105,315)
(106,314)(107,313)(108,326)(109,325)(110,331)(111,330)(112,329)(113,328)
(114,327)(115,319)(116,318)(117,324)(118,323)(119,322)(120,321)(121,320)
(122,333)(123,332)(124,338)(125,337)(126,336)(127,335)(128,334)(129,263)
(130,262)(131,268)(132,267)(133,266)(134,265)(135,264)(136,256)(137,255)
(138,261)(139,260)(140,259)(141,258)(142,257)(143,270)(144,269)(145,275)
(146,274)(147,273)(148,272)(149,271)(150,284)(151,283)(152,289)(153,288)
(154,287)(155,286)(156,285)(157,277)(158,276)(159,282)(160,281)(161,280)
(162,279)(163,278)(164,291)(165,290)(166,296)(167,295)(168,294)(169,293)
(170,292);
poly := sub<Sym(338)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope