Polytope of Type {2,312}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,312}*1248
if this polytope has a name.
Group : SmallGroup(1248,1077)
Rank : 3
Schlafli Type : {2,312}
Number of vertices, edges, etc : 2, 312, 312
Order of s₀s₁s₂ : 312
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 : {2,156}*624
   3-fold quotients : {2,104}*416
   4-fold quotients : {2,78}*312
   6-fold quotients : {2,52}*208
   8-fold quotients : {2,39}*156
   12-fold quotients : {2,26}*104
   13-fold quotients : {2,24}*96
   24-fold quotients : {2,13}*52
   26-fold quotients : {2,12}*48
   39-fold quotients : {2,8}*32
   52-fold quotients : {2,6}*24
   78-fold quotients : {2,4}*16
   104-fold quotients : {2,3}*12
   156-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope