Polytope of Type {2,330}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,330}*1320
if this polytope has a name.
Group : SmallGroup(1320,180)
Rank : 3
Schlafli Type : {2,330}
Number of vertices, edges, etc : 2, 330, 330
Order of s₀s₁s₂ : 330
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 : {2,165}*660
   3-fold quotients : {2,110}*440
   5-fold quotients : {2,66}*264
   6-fold quotients : {2,55}*220
   10-fold quotients : {2,33}*132
   11-fold quotients : {2,30}*120
   15-fold quotients : {2,22}*88
   22-fold quotients : {2,15}*60
   30-fold quotients : {2,11}*44
   33-fold quotients : {2,10}*40
   55-fold quotients : {2,6}*24
   66-fold quotients : {2,5}*20
   110-fold quotients : {2,3}*12
   165-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope