Polytope of Type {304,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {304,2}*1216
if this polytope has a name.
Group : SmallGroup(1216,970)
Rank : 3
Schlafli Type : {304,2}
Number of vertices, edges, etc : 304, 304, 2
Order of s₀s₁s₂ : 304
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {152,2}*608
   4-fold quotients : {76,2}*304
   8-fold quotients : {38,2}*152
   16-fold quotients : {19,2}*76
   19-fold quotients : {16,2}*64
   38-fold quotients : {8,2}*32
   76-fold quotients : {4,2}*16
   152-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope