Polytope of Type {2,320}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,320}*1280
if this polytope has a name.
Group : SmallGroup(1280,90611)
Rank : 3
Schlafli Type : {2,320}
Number of vertices, edges, etc : 2, 320, 320
Order of s₀s₁s₂ : 320
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 : {2,160}*640
   4-fold quotients : {2,80}*320
   5-fold quotients : {2,64}*256
   8-fold quotients : {2,40}*160
   10-fold quotients : {2,32}*128
   16-fold quotients : {2,20}*80
   20-fold quotients : {2,16}*64
   32-fold quotients : {2,10}*40
   40-fold quotients : {2,8}*32
   64-fold quotients : {2,5}*20
   80-fold quotients : {2,4}*16
   160-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope