Polytope of Type {4,154}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,154}*1232
Also Known As : {4,154|2}. if this polytope has another name.
Group : SmallGroup(1232,137)
Rank : 3
Schlafli Type : {4,154}
Number of vertices, edges, etc : 4, 308, 154
Order of s₀s₁s₂ : 308
Order of s₀s₁s₂s₁ : 2
Special Properties :
   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 : {2,154}*616
   4-fold quotients : {2,77}*308
   7-fold quotients : {4,22}*176
   11-fold quotients : {4,14}*112
   14-fold quotients : {2,22}*88
   22-fold quotients : {2,14}*56
   28-fold quotients : {2,11}*44
   44-fold quotients : {2,7}*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 := (155,232)(156,233)(157,234)(158,235)(159,236)(160,237)(161,238)(162,239)
(163,240)(164,241)(165,242)(166,243)(167,244)(168,245)(169,246)(170,247)
(171,248)(172,249)(173,250)(174,251)(175,252)(176,253)(177,254)(178,255)
(179,256)(180,257)(181,258)(182,259)(183,260)(184,261)(185,262)(186,263)
(187,264)(188,265)(189,266)(190,267)(191,268)(192,269)(193,270)(194,271)
(195,272)(196,273)(197,274)(198,275)(199,276)(200,277)(201,278)(202,279)
(203,280)(204,281)(205,282)(206,283)(207,284)(208,285)(209,286)(210,287)
(211,288)(212,289)(213,290)(214,291)(215,292)(216,293)(217,294)(218,295)
(219,296)(220,297)(221,298)(222,299)(223,300)(224,301)(225,302)(226,303)
(227,304)(228,305)(229,306)(230,307)(231,308);;
s1 := (  1,155)(  2,165)(  3,164)(  4,163)(  5,162)(  6,161)(  7,160)(  8,159)
(  9,158)( 10,157)( 11,156)( 12,221)( 13,231)( 14,230)( 15,229)( 16,228)
( 17,227)( 18,226)( 19,225)( 20,224)( 21,223)( 22,222)( 23,210)( 24,220)
( 25,219)( 26,218)( 27,217)( 28,216)( 29,215)( 30,214)( 31,213)( 32,212)
( 33,211)( 34,199)( 35,209)( 36,208)( 37,207)( 38,206)( 39,205)( 40,204)
( 41,203)( 42,202)( 43,201)( 44,200)( 45,188)( 46,198)( 47,197)( 48,196)
( 49,195)( 50,194)( 51,193)( 52,192)( 53,191)( 54,190)( 55,189)( 56,177)
( 57,187)( 58,186)( 59,185)( 60,184)( 61,183)( 62,182)( 63,181)( 64,180)
( 65,179)( 66,178)( 67,166)( 68,176)( 69,175)( 70,174)( 71,173)( 72,172)
( 73,171)( 74,170)( 75,169)( 76,168)( 77,167)( 78,232)( 79,242)( 80,241)
( 81,240)( 82,239)( 83,238)( 84,237)( 85,236)( 86,235)( 87,234)( 88,233)
( 89,298)( 90,308)( 91,307)( 92,306)( 93,305)( 94,304)( 95,303)( 96,302)
( 97,301)( 98,300)( 99,299)(100,287)(101,297)(102,296)(103,295)(104,294)
(105,293)(106,292)(107,291)(108,290)(109,289)(110,288)(111,276)(112,286)
(113,285)(114,284)(115,283)(116,282)(117,281)(118,280)(119,279)(120,278)
(121,277)(122,265)(123,275)(124,274)(125,273)(126,272)(127,271)(128,270)
(129,269)(130,268)(131,267)(132,266)(133,254)(134,264)(135,263)(136,262)
(137,261)(138,260)(139,259)(140,258)(141,257)(142,256)(143,255)(144,243)
(145,253)(146,252)(147,251)(148,250)(149,249)(150,248)(151,247)(152,246)
(153,245)(154,244);;
s2 := (  1, 13)(  2, 12)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)
(  9, 16)( 10, 15)( 11, 14)( 23, 68)( 24, 67)( 25, 77)( 26, 76)( 27, 75)
( 28, 74)( 29, 73)( 30, 72)( 31, 71)( 32, 70)( 33, 69)( 34, 57)( 35, 56)
( 36, 66)( 37, 65)( 38, 64)( 39, 63)( 40, 62)( 41, 61)( 42, 60)( 43, 59)
( 44, 58)( 45, 46)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 78, 90)( 79, 89)
( 80, 99)( 81, 98)( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)
( 88, 91)(100,145)(101,144)(102,154)(103,153)(104,152)(105,151)(106,150)
(107,149)(108,148)(109,147)(110,146)(111,134)(112,133)(113,143)(114,142)
(115,141)(116,140)(117,139)(118,138)(119,137)(120,136)(121,135)(122,123)
(124,132)(125,131)(126,130)(127,129)(155,167)(156,166)(157,176)(158,175)
(159,174)(160,173)(161,172)(162,171)(163,170)(164,169)(165,168)(177,222)
(178,221)(179,231)(180,230)(181,229)(182,228)(183,227)(184,226)(185,225)
(186,224)(187,223)(188,211)(189,210)(190,220)(191,219)(192,218)(193,217)
(194,216)(195,215)(196,214)(197,213)(198,212)(199,200)(201,209)(202,208)
(203,207)(204,206)(232,244)(233,243)(234,253)(235,252)(236,251)(237,250)
(238,249)(239,248)(240,247)(241,246)(242,245)(254,299)(255,298)(256,308)
(257,307)(258,306)(259,305)(260,304)(261,303)(262,302)(263,301)(264,300)
(265,288)(266,287)(267,297)(268,296)(269,295)(270,294)(271,293)(272,292)
(273,291)(274,290)(275,289)(276,277)(278,286)(279,285)(280,284)(281,283);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(308)!(155,232)(156,233)(157,234)(158,235)(159,236)(160,237)(161,238)
(162,239)(163,240)(164,241)(165,242)(166,243)(167,244)(168,245)(169,246)
(170,247)(171,248)(172,249)(173,250)(174,251)(175,252)(176,253)(177,254)
(178,255)(179,256)(180,257)(181,258)(182,259)(183,260)(184,261)(185,262)
(186,263)(187,264)(188,265)(189,266)(190,267)(191,268)(192,269)(193,270)
(194,271)(195,272)(196,273)(197,274)(198,275)(199,276)(200,277)(201,278)
(202,279)(203,280)(204,281)(205,282)(206,283)(207,284)(208,285)(209,286)
(210,287)(211,288)(212,289)(213,290)(214,291)(215,292)(216,293)(217,294)
(218,295)(219,296)(220,297)(221,298)(222,299)(223,300)(224,301)(225,302)
(226,303)(227,304)(228,305)(229,306)(230,307)(231,308);
s1 := Sym(308)!(  1,155)(  2,165)(  3,164)(  4,163)(  5,162)(  6,161)(  7,160)
(  8,159)(  9,158)( 10,157)( 11,156)( 12,221)( 13,231)( 14,230)( 15,229)
( 16,228)( 17,227)( 18,226)( 19,225)( 20,224)( 21,223)( 22,222)( 23,210)
( 24,220)( 25,219)( 26,218)( 27,217)( 28,216)( 29,215)( 30,214)( 31,213)
( 32,212)( 33,211)( 34,199)( 35,209)( 36,208)( 37,207)( 38,206)( 39,205)
( 40,204)( 41,203)( 42,202)( 43,201)( 44,200)( 45,188)( 46,198)( 47,197)
( 48,196)( 49,195)( 50,194)( 51,193)( 52,192)( 53,191)( 54,190)( 55,189)
( 56,177)( 57,187)( 58,186)( 59,185)( 60,184)( 61,183)( 62,182)( 63,181)
( 64,180)( 65,179)( 66,178)( 67,166)( 68,176)( 69,175)( 70,174)( 71,173)
( 72,172)( 73,171)( 74,170)( 75,169)( 76,168)( 77,167)( 78,232)( 79,242)
( 80,241)( 81,240)( 82,239)( 83,238)( 84,237)( 85,236)( 86,235)( 87,234)
( 88,233)( 89,298)( 90,308)( 91,307)( 92,306)( 93,305)( 94,304)( 95,303)
( 96,302)( 97,301)( 98,300)( 99,299)(100,287)(101,297)(102,296)(103,295)
(104,294)(105,293)(106,292)(107,291)(108,290)(109,289)(110,288)(111,276)
(112,286)(113,285)(114,284)(115,283)(116,282)(117,281)(118,280)(119,279)
(120,278)(121,277)(122,265)(123,275)(124,274)(125,273)(126,272)(127,271)
(128,270)(129,269)(130,268)(131,267)(132,266)(133,254)(134,264)(135,263)
(136,262)(137,261)(138,260)(139,259)(140,258)(141,257)(142,256)(143,255)
(144,243)(145,253)(146,252)(147,251)(148,250)(149,249)(150,248)(151,247)
(152,246)(153,245)(154,244);
s2 := Sym(308)!(  1, 13)(  2, 12)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)
(  8, 17)(  9, 16)( 10, 15)( 11, 14)( 23, 68)( 24, 67)( 25, 77)( 26, 76)
( 27, 75)( 28, 74)( 29, 73)( 30, 72)( 31, 71)( 32, 70)( 33, 69)( 34, 57)
( 35, 56)( 36, 66)( 37, 65)( 38, 64)( 39, 63)( 40, 62)( 41, 61)( 42, 60)
( 43, 59)( 44, 58)( 45, 46)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 78, 90)
( 79, 89)( 80, 99)( 81, 98)( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)
( 87, 92)( 88, 91)(100,145)(101,144)(102,154)(103,153)(104,152)(105,151)
(106,150)(107,149)(108,148)(109,147)(110,146)(111,134)(112,133)(113,143)
(114,142)(115,141)(116,140)(117,139)(118,138)(119,137)(120,136)(121,135)
(122,123)(124,132)(125,131)(126,130)(127,129)(155,167)(156,166)(157,176)
(158,175)(159,174)(160,173)(161,172)(162,171)(163,170)(164,169)(165,168)
(177,222)(178,221)(179,231)(180,230)(181,229)(182,228)(183,227)(184,226)
(185,225)(186,224)(187,223)(188,211)(189,210)(190,220)(191,219)(192,218)
(193,217)(194,216)(195,215)(196,214)(197,213)(198,212)(199,200)(201,209)
(202,208)(203,207)(204,206)(232,244)(233,243)(234,253)(235,252)(236,251)
(237,250)(238,249)(239,248)(240,247)(241,246)(242,245)(254,299)(255,298)
(256,308)(257,307)(258,306)(259,305)(260,304)(261,303)(262,302)(263,301)
(264,300)(265,288)(266,287)(267,297)(268,296)(269,295)(270,294)(271,293)
(272,292)(273,291)(274,290)(275,289)(276,277)(278,286)(279,285)(280,284)
(281,283);
poly := sub<Sym(308)|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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope