Polytope of Type {154,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {154,4}*1232
Also Known As : {154,4|2}. if this polytope has another name.
Group : SmallGroup(1232,137)
Rank : 3
Schlafli Type : {154,4}
Number of vertices, edges, etc : 154, 308, 4
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 : {154,2}*616
4-fold quotients : {77,2}*308
7-fold quotients : {22,4}*176
11-fold quotients : {14,4}*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 : {2,4}*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)(156,165)(157,164)(158,163)(159,162)
(160,161)(166,221)(167,231)(168,230)(169,229)(170,228)(171,227)(172,226)
(173,225)(174,224)(175,223)(176,222)(177,210)(178,220)(179,219)(180,218)
(181,217)(182,216)(183,215)(184,214)(185,213)(186,212)(187,211)(188,199)
(189,209)(190,208)(191,207)(192,206)(193,205)(194,204)(195,203)(196,202)
(197,201)(198,200)(233,242)(234,241)(235,240)(236,239)(237,238)(243,298)
(244,308)(245,307)(246,306)(247,305)(248,304)(249,303)(250,302)(251,301)
(252,300)(253,299)(254,287)(255,297)(256,296)(257,295)(258,294)(259,293)
(260,292)(261,291)(262,290)(263,289)(264,288)(265,276)(266,286)(267,285)
(268,284)(269,283)(270,282)(271,281)(272,280)(273,279)(274,278)(275,277);;
s1 := ( 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)(155,244)(156,243)(157,253)(158,252)
(159,251)(160,250)(161,249)(162,248)(163,247)(164,246)(165,245)(166,233)
(167,232)(168,242)(169,241)(170,240)(171,239)(172,238)(173,237)(174,236)
(175,235)(176,234)(177,299)(178,298)(179,308)(180,307)(181,306)(182,305)
(183,304)(184,303)(185,302)(186,301)(187,300)(188,288)(189,287)(190,297)
(191,296)(192,295)(193,294)(194,293)(195,292)(196,291)(197,290)(198,289)
(199,277)(200,276)(201,286)(202,285)(203,284)(204,283)(205,282)(206,281)
(207,280)(208,279)(209,278)(210,266)(211,265)(212,275)(213,274)(214,273)
(215,272)(216,271)(217,270)(218,269)(219,268)(220,267)(221,255)(222,254)
(223,264)(224,263)(225,262)(226,261)(227,260)(228,259)(229,258)(230,257)
(231,256);;
s2 := ( 1,155)( 2,156)( 3,157)( 4,158)( 5,159)( 6,160)( 7,161)( 8,162)
( 9,163)( 10,164)( 11,165)( 12,166)( 13,167)( 14,168)( 15,169)( 16,170)
( 17,171)( 18,172)( 19,173)( 20,174)( 21,175)( 22,176)( 23,177)( 24,178)
( 25,179)( 26,180)( 27,181)( 28,182)( 29,183)( 30,184)( 31,185)( 32,186)
( 33,187)( 34,188)( 35,189)( 36,190)( 37,191)( 38,192)( 39,193)( 40,194)
( 41,195)( 42,196)( 43,197)( 44,198)( 45,199)( 46,200)( 47,201)( 48,202)
( 49,203)( 50,204)( 51,205)( 52,206)( 53,207)( 54,208)( 55,209)( 56,210)
( 57,211)( 58,212)( 59,213)( 60,214)( 61,215)( 62,216)( 63,217)( 64,218)
( 65,219)( 66,220)( 67,221)( 68,222)( 69,223)( 70,224)( 71,225)( 72,226)
( 73,227)( 74,228)( 75,229)( 76,230)( 77,231)( 78,232)( 79,233)( 80,234)
( 81,235)( 82,236)( 83,237)( 84,238)( 85,239)( 86,240)( 87,241)( 88,242)
( 89,243)( 90,244)( 91,245)( 92,246)( 93,247)( 94,248)( 95,249)( 96,250)
( 97,251)( 98,252)( 99,253)(100,254)(101,255)(102,256)(103,257)(104,258)
(105,259)(106,260)(107,261)(108,262)(109,263)(110,264)(111,265)(112,266)
(113,267)(114,268)(115,269)(116,270)(117,271)(118,272)(119,273)(120,274)
(121,275)(122,276)(123,277)(124,278)(125,279)(126,280)(127,281)(128,282)
(129,283)(130,284)(131,285)(132,286)(133,287)(134,288)(135,289)(136,290)
(137,291)(138,292)(139,293)(140,294)(141,295)(142,296)(143,297)(144,298)
(145,299)(146,300)(147,301)(148,302)(149,303)(150,304)(151,305)(152,306)
(153,307)(154,308);;
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(308)!( 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)(156,165)(157,164)(158,163)
(159,162)(160,161)(166,221)(167,231)(168,230)(169,229)(170,228)(171,227)
(172,226)(173,225)(174,224)(175,223)(176,222)(177,210)(178,220)(179,219)
(180,218)(181,217)(182,216)(183,215)(184,214)(185,213)(186,212)(187,211)
(188,199)(189,209)(190,208)(191,207)(192,206)(193,205)(194,204)(195,203)
(196,202)(197,201)(198,200)(233,242)(234,241)(235,240)(236,239)(237,238)
(243,298)(244,308)(245,307)(246,306)(247,305)(248,304)(249,303)(250,302)
(251,301)(252,300)(253,299)(254,287)(255,297)(256,296)(257,295)(258,294)
(259,293)(260,292)(261,291)(262,290)(263,289)(264,288)(265,276)(266,286)
(267,285)(268,284)(269,283)(270,282)(271,281)(272,280)(273,279)(274,278)
(275,277);
s1 := 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)(155,244)(156,243)(157,253)
(158,252)(159,251)(160,250)(161,249)(162,248)(163,247)(164,246)(165,245)
(166,233)(167,232)(168,242)(169,241)(170,240)(171,239)(172,238)(173,237)
(174,236)(175,235)(176,234)(177,299)(178,298)(179,308)(180,307)(181,306)
(182,305)(183,304)(184,303)(185,302)(186,301)(187,300)(188,288)(189,287)
(190,297)(191,296)(192,295)(193,294)(194,293)(195,292)(196,291)(197,290)
(198,289)(199,277)(200,276)(201,286)(202,285)(203,284)(204,283)(205,282)
(206,281)(207,280)(208,279)(209,278)(210,266)(211,265)(212,275)(213,274)
(214,273)(215,272)(216,271)(217,270)(218,269)(219,268)(220,267)(221,255)
(222,254)(223,264)(224,263)(225,262)(226,261)(227,260)(228,259)(229,258)
(230,257)(231,256);
s2 := Sym(308)!( 1,155)( 2,156)( 3,157)( 4,158)( 5,159)( 6,160)( 7,161)
( 8,162)( 9,163)( 10,164)( 11,165)( 12,166)( 13,167)( 14,168)( 15,169)
( 16,170)( 17,171)( 18,172)( 19,173)( 20,174)( 21,175)( 22,176)( 23,177)
( 24,178)( 25,179)( 26,180)( 27,181)( 28,182)( 29,183)( 30,184)( 31,185)
( 32,186)( 33,187)( 34,188)( 35,189)( 36,190)( 37,191)( 38,192)( 39,193)
( 40,194)( 41,195)( 42,196)( 43,197)( 44,198)( 45,199)( 46,200)( 47,201)
( 48,202)( 49,203)( 50,204)( 51,205)( 52,206)( 53,207)( 54,208)( 55,209)
( 56,210)( 57,211)( 58,212)( 59,213)( 60,214)( 61,215)( 62,216)( 63,217)
( 64,218)( 65,219)( 66,220)( 67,221)( 68,222)( 69,223)( 70,224)( 71,225)
( 72,226)( 73,227)( 74,228)( 75,229)( 76,230)( 77,231)( 78,232)( 79,233)
( 80,234)( 81,235)( 82,236)( 83,237)( 84,238)( 85,239)( 86,240)( 87,241)
( 88,242)( 89,243)( 90,244)( 91,245)( 92,246)( 93,247)( 94,248)( 95,249)
( 96,250)( 97,251)( 98,252)( 99,253)(100,254)(101,255)(102,256)(103,257)
(104,258)(105,259)(106,260)(107,261)(108,262)(109,263)(110,264)(111,265)
(112,266)(113,267)(114,268)(115,269)(116,270)(117,271)(118,272)(119,273)
(120,274)(121,275)(122,276)(123,277)(124,278)(125,279)(126,280)(127,281)
(128,282)(129,283)(130,284)(131,285)(132,286)(133,287)(134,288)(135,289)
(136,290)(137,291)(138,292)(139,293)(140,294)(141,295)(142,296)(143,297)
(144,298)(145,299)(146,300)(147,301)(148,302)(149,303)(150,304)(151,305)
(152,306)(153,307)(154,308);
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*s2*s1*s0*s1*s2*s1,
s1*s2*s1*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 >;
References : None.
to this polytope