Polytope of Type {308,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {308,2}*1232
if this polytope has a name.
Group : SmallGroup(1232,135)
Rank : 3
Schlafli Type : {308,2}
Number of vertices, edges, etc : 308, 308, 2
Order of s₀s₁s₂ : 308
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 : {154,2}*616
   4-fold quotients : {77,2}*308
   7-fold quotients : {44,2}*176
   11-fold quotients : {28,2}*112
   14-fold quotients : {22,2}*88
   22-fold quotients : {14,2}*56
   28-fold quotients : {11,2}*44
   44-fold quotients : {7,2}*28
   77-fold quotients : {4,2}*16
   154-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope