Polytope of Type {146,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {146,6}*1752
Also Known As : {146,6|2}. if this polytope has another name.
Group : SmallGroup(1752,57)
Rank : 3
Schlafli Type : {146,6}
Number of vertices, edges, etc : 146, 438, 6
Order of s0s1s2 : 438
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) :
3-fold quotients : {146,2}*584
6-fold quotients : {73,2}*292
73-fold quotients : {2,6}*24
146-fold quotients : {2,3}*12
219-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 73)( 3, 72)( 4, 71)( 5, 70)( 6, 69)( 7, 68)( 8, 67)( 9, 66)
( 10, 65)( 11, 64)( 12, 63)( 13, 62)( 14, 61)( 15, 60)( 16, 59)( 17, 58)
( 18, 57)( 19, 56)( 20, 55)( 21, 54)( 22, 53)( 23, 52)( 24, 51)( 25, 50)
( 26, 49)( 27, 48)( 28, 47)( 29, 46)( 30, 45)( 31, 44)( 32, 43)( 33, 42)
( 34, 41)( 35, 40)( 36, 39)( 37, 38)( 75,146)( 76,145)( 77,144)( 78,143)
( 79,142)( 80,141)( 81,140)( 82,139)( 83,138)( 84,137)( 85,136)( 86,135)
( 87,134)( 88,133)( 89,132)( 90,131)( 91,130)( 92,129)( 93,128)( 94,127)
( 95,126)( 96,125)( 97,124)( 98,123)( 99,122)(100,121)(101,120)(102,119)
(103,118)(104,117)(105,116)(106,115)(107,114)(108,113)(109,112)(110,111)
(148,219)(149,218)(150,217)(151,216)(152,215)(153,214)(154,213)(155,212)
(156,211)(157,210)(158,209)(159,208)(160,207)(161,206)(162,205)(163,204)
(164,203)(165,202)(166,201)(167,200)(168,199)(169,198)(170,197)(171,196)
(172,195)(173,194)(174,193)(175,192)(176,191)(177,190)(178,189)(179,188)
(180,187)(181,186)(182,185)(183,184)(221,292)(222,291)(223,290)(224,289)
(225,288)(226,287)(227,286)(228,285)(229,284)(230,283)(231,282)(232,281)
(233,280)(234,279)(235,278)(236,277)(237,276)(238,275)(239,274)(240,273)
(241,272)(242,271)(243,270)(244,269)(245,268)(246,267)(247,266)(248,265)
(249,264)(250,263)(251,262)(252,261)(253,260)(254,259)(255,258)(256,257)
(294,365)(295,364)(296,363)(297,362)(298,361)(299,360)(300,359)(301,358)
(302,357)(303,356)(304,355)(305,354)(306,353)(307,352)(308,351)(309,350)
(310,349)(311,348)(312,347)(313,346)(314,345)(315,344)(316,343)(317,342)
(318,341)(319,340)(320,339)(321,338)(322,337)(323,336)(324,335)(325,334)
(326,333)(327,332)(328,331)(329,330)(367,438)(368,437)(369,436)(370,435)
(371,434)(372,433)(373,432)(374,431)(375,430)(376,429)(377,428)(378,427)
(379,426)(380,425)(381,424)(382,423)(383,422)(384,421)(385,420)(386,419)
(387,418)(388,417)(389,416)(390,415)(391,414)(392,413)(393,412)(394,411)
(395,410)(396,409)(397,408)(398,407)(399,406)(400,405)(401,404)(402,403);;
s1 := ( 1, 2)( 3, 73)( 4, 72)( 5, 71)( 6, 70)( 7, 69)( 8, 68)( 9, 67)
( 10, 66)( 11, 65)( 12, 64)( 13, 63)( 14, 62)( 15, 61)( 16, 60)( 17, 59)
( 18, 58)( 19, 57)( 20, 56)( 21, 55)( 22, 54)( 23, 53)( 24, 52)( 25, 51)
( 26, 50)( 27, 49)( 28, 48)( 29, 47)( 30, 46)( 31, 45)( 32, 44)( 33, 43)
( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 74,148)( 75,147)( 76,219)( 77,218)
( 78,217)( 79,216)( 80,215)( 81,214)( 82,213)( 83,212)( 84,211)( 85,210)
( 86,209)( 87,208)( 88,207)( 89,206)( 90,205)( 91,204)( 92,203)( 93,202)
( 94,201)( 95,200)( 96,199)( 97,198)( 98,197)( 99,196)(100,195)(101,194)
(102,193)(103,192)(104,191)(105,190)(106,189)(107,188)(108,187)(109,186)
(110,185)(111,184)(112,183)(113,182)(114,181)(115,180)(116,179)(117,178)
(118,177)(119,176)(120,175)(121,174)(122,173)(123,172)(124,171)(125,170)
(126,169)(127,168)(128,167)(129,166)(130,165)(131,164)(132,163)(133,162)
(134,161)(135,160)(136,159)(137,158)(138,157)(139,156)(140,155)(141,154)
(142,153)(143,152)(144,151)(145,150)(146,149)(220,221)(222,292)(223,291)
(224,290)(225,289)(226,288)(227,287)(228,286)(229,285)(230,284)(231,283)
(232,282)(233,281)(234,280)(235,279)(236,278)(237,277)(238,276)(239,275)
(240,274)(241,273)(242,272)(243,271)(244,270)(245,269)(246,268)(247,267)
(248,266)(249,265)(250,264)(251,263)(252,262)(253,261)(254,260)(255,259)
(256,258)(293,367)(294,366)(295,438)(296,437)(297,436)(298,435)(299,434)
(300,433)(301,432)(302,431)(303,430)(304,429)(305,428)(306,427)(307,426)
(308,425)(309,424)(310,423)(311,422)(312,421)(313,420)(314,419)(315,418)
(316,417)(317,416)(318,415)(319,414)(320,413)(321,412)(322,411)(323,410)
(324,409)(325,408)(326,407)(327,406)(328,405)(329,404)(330,403)(331,402)
(332,401)(333,400)(334,399)(335,398)(336,397)(337,396)(338,395)(339,394)
(340,393)(341,392)(342,391)(343,390)(344,389)(345,388)(346,387)(347,386)
(348,385)(349,384)(350,383)(351,382)(352,381)(353,380)(354,379)(355,378)
(356,377)(357,376)(358,375)(359,374)(360,373)(361,372)(362,371)(363,370)
(364,369)(365,368);;
s2 := ( 1,293)( 2,294)( 3,295)( 4,296)( 5,297)( 6,298)( 7,299)( 8,300)
( 9,301)( 10,302)( 11,303)( 12,304)( 13,305)( 14,306)( 15,307)( 16,308)
( 17,309)( 18,310)( 19,311)( 20,312)( 21,313)( 22,314)( 23,315)( 24,316)
( 25,317)( 26,318)( 27,319)( 28,320)( 29,321)( 30,322)( 31,323)( 32,324)
( 33,325)( 34,326)( 35,327)( 36,328)( 37,329)( 38,330)( 39,331)( 40,332)
( 41,333)( 42,334)( 43,335)( 44,336)( 45,337)( 46,338)( 47,339)( 48,340)
( 49,341)( 50,342)( 51,343)( 52,344)( 53,345)( 54,346)( 55,347)( 56,348)
( 57,349)( 58,350)( 59,351)( 60,352)( 61,353)( 62,354)( 63,355)( 64,356)
( 65,357)( 66,358)( 67,359)( 68,360)( 69,361)( 70,362)( 71,363)( 72,364)
( 73,365)( 74,220)( 75,221)( 76,222)( 77,223)( 78,224)( 79,225)( 80,226)
( 81,227)( 82,228)( 83,229)( 84,230)( 85,231)( 86,232)( 87,233)( 88,234)
( 89,235)( 90,236)( 91,237)( 92,238)( 93,239)( 94,240)( 95,241)( 96,242)
( 97,243)( 98,244)( 99,245)(100,246)(101,247)(102,248)(103,249)(104,250)
(105,251)(106,252)(107,253)(108,254)(109,255)(110,256)(111,257)(112,258)
(113,259)(114,260)(115,261)(116,262)(117,263)(118,264)(119,265)(120,266)
(121,267)(122,268)(123,269)(124,270)(125,271)(126,272)(127,273)(128,274)
(129,275)(130,276)(131,277)(132,278)(133,279)(134,280)(135,281)(136,282)
(137,283)(138,284)(139,285)(140,286)(141,287)(142,288)(143,289)(144,290)
(145,291)(146,292)(147,366)(148,367)(149,368)(150,369)(151,370)(152,371)
(153,372)(154,373)(155,374)(156,375)(157,376)(158,377)(159,378)(160,379)
(161,380)(162,381)(163,382)(164,383)(165,384)(166,385)(167,386)(168,387)
(169,388)(170,389)(171,390)(172,391)(173,392)(174,393)(175,394)(176,395)
(177,396)(178,397)(179,398)(180,399)(181,400)(182,401)(183,402)(184,403)
(185,404)(186,405)(187,406)(188,407)(189,408)(190,409)(191,410)(192,411)
(193,412)(194,413)(195,414)(196,415)(197,416)(198,417)(199,418)(200,419)
(201,420)(202,421)(203,422)(204,423)(205,424)(206,425)(207,426)(208,427)
(209,428)(210,429)(211,430)(212,431)(213,432)(214,433)(215,434)(216,435)
(217,436)(218,437)(219,438);;
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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(438)!( 2, 73)( 3, 72)( 4, 71)( 5, 70)( 6, 69)( 7, 68)( 8, 67)
( 9, 66)( 10, 65)( 11, 64)( 12, 63)( 13, 62)( 14, 61)( 15, 60)( 16, 59)
( 17, 58)( 18, 57)( 19, 56)( 20, 55)( 21, 54)( 22, 53)( 23, 52)( 24, 51)
( 25, 50)( 26, 49)( 27, 48)( 28, 47)( 29, 46)( 30, 45)( 31, 44)( 32, 43)
( 33, 42)( 34, 41)( 35, 40)( 36, 39)( 37, 38)( 75,146)( 76,145)( 77,144)
( 78,143)( 79,142)( 80,141)( 81,140)( 82,139)( 83,138)( 84,137)( 85,136)
( 86,135)( 87,134)( 88,133)( 89,132)( 90,131)( 91,130)( 92,129)( 93,128)
( 94,127)( 95,126)( 96,125)( 97,124)( 98,123)( 99,122)(100,121)(101,120)
(102,119)(103,118)(104,117)(105,116)(106,115)(107,114)(108,113)(109,112)
(110,111)(148,219)(149,218)(150,217)(151,216)(152,215)(153,214)(154,213)
(155,212)(156,211)(157,210)(158,209)(159,208)(160,207)(161,206)(162,205)
(163,204)(164,203)(165,202)(166,201)(167,200)(168,199)(169,198)(170,197)
(171,196)(172,195)(173,194)(174,193)(175,192)(176,191)(177,190)(178,189)
(179,188)(180,187)(181,186)(182,185)(183,184)(221,292)(222,291)(223,290)
(224,289)(225,288)(226,287)(227,286)(228,285)(229,284)(230,283)(231,282)
(232,281)(233,280)(234,279)(235,278)(236,277)(237,276)(238,275)(239,274)
(240,273)(241,272)(242,271)(243,270)(244,269)(245,268)(246,267)(247,266)
(248,265)(249,264)(250,263)(251,262)(252,261)(253,260)(254,259)(255,258)
(256,257)(294,365)(295,364)(296,363)(297,362)(298,361)(299,360)(300,359)
(301,358)(302,357)(303,356)(304,355)(305,354)(306,353)(307,352)(308,351)
(309,350)(310,349)(311,348)(312,347)(313,346)(314,345)(315,344)(316,343)
(317,342)(318,341)(319,340)(320,339)(321,338)(322,337)(323,336)(324,335)
(325,334)(326,333)(327,332)(328,331)(329,330)(367,438)(368,437)(369,436)
(370,435)(371,434)(372,433)(373,432)(374,431)(375,430)(376,429)(377,428)
(378,427)(379,426)(380,425)(381,424)(382,423)(383,422)(384,421)(385,420)
(386,419)(387,418)(388,417)(389,416)(390,415)(391,414)(392,413)(393,412)
(394,411)(395,410)(396,409)(397,408)(398,407)(399,406)(400,405)(401,404)
(402,403);
s1 := Sym(438)!( 1, 2)( 3, 73)( 4, 72)( 5, 71)( 6, 70)( 7, 69)( 8, 68)
( 9, 67)( 10, 66)( 11, 65)( 12, 64)( 13, 63)( 14, 62)( 15, 61)( 16, 60)
( 17, 59)( 18, 58)( 19, 57)( 20, 56)( 21, 55)( 22, 54)( 23, 53)( 24, 52)
( 25, 51)( 26, 50)( 27, 49)( 28, 48)( 29, 47)( 30, 46)( 31, 45)( 32, 44)
( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 74,148)( 75,147)( 76,219)
( 77,218)( 78,217)( 79,216)( 80,215)( 81,214)( 82,213)( 83,212)( 84,211)
( 85,210)( 86,209)( 87,208)( 88,207)( 89,206)( 90,205)( 91,204)( 92,203)
( 93,202)( 94,201)( 95,200)( 96,199)( 97,198)( 98,197)( 99,196)(100,195)
(101,194)(102,193)(103,192)(104,191)(105,190)(106,189)(107,188)(108,187)
(109,186)(110,185)(111,184)(112,183)(113,182)(114,181)(115,180)(116,179)
(117,178)(118,177)(119,176)(120,175)(121,174)(122,173)(123,172)(124,171)
(125,170)(126,169)(127,168)(128,167)(129,166)(130,165)(131,164)(132,163)
(133,162)(134,161)(135,160)(136,159)(137,158)(138,157)(139,156)(140,155)
(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(220,221)(222,292)
(223,291)(224,290)(225,289)(226,288)(227,287)(228,286)(229,285)(230,284)
(231,283)(232,282)(233,281)(234,280)(235,279)(236,278)(237,277)(238,276)
(239,275)(240,274)(241,273)(242,272)(243,271)(244,270)(245,269)(246,268)
(247,267)(248,266)(249,265)(250,264)(251,263)(252,262)(253,261)(254,260)
(255,259)(256,258)(293,367)(294,366)(295,438)(296,437)(297,436)(298,435)
(299,434)(300,433)(301,432)(302,431)(303,430)(304,429)(305,428)(306,427)
(307,426)(308,425)(309,424)(310,423)(311,422)(312,421)(313,420)(314,419)
(315,418)(316,417)(317,416)(318,415)(319,414)(320,413)(321,412)(322,411)
(323,410)(324,409)(325,408)(326,407)(327,406)(328,405)(329,404)(330,403)
(331,402)(332,401)(333,400)(334,399)(335,398)(336,397)(337,396)(338,395)
(339,394)(340,393)(341,392)(342,391)(343,390)(344,389)(345,388)(346,387)
(347,386)(348,385)(349,384)(350,383)(351,382)(352,381)(353,380)(354,379)
(355,378)(356,377)(357,376)(358,375)(359,374)(360,373)(361,372)(362,371)
(363,370)(364,369)(365,368);
s2 := Sym(438)!( 1,293)( 2,294)( 3,295)( 4,296)( 5,297)( 6,298)( 7,299)
( 8,300)( 9,301)( 10,302)( 11,303)( 12,304)( 13,305)( 14,306)( 15,307)
( 16,308)( 17,309)( 18,310)( 19,311)( 20,312)( 21,313)( 22,314)( 23,315)
( 24,316)( 25,317)( 26,318)( 27,319)( 28,320)( 29,321)( 30,322)( 31,323)
( 32,324)( 33,325)( 34,326)( 35,327)( 36,328)( 37,329)( 38,330)( 39,331)
( 40,332)( 41,333)( 42,334)( 43,335)( 44,336)( 45,337)( 46,338)( 47,339)
( 48,340)( 49,341)( 50,342)( 51,343)( 52,344)( 53,345)( 54,346)( 55,347)
( 56,348)( 57,349)( 58,350)( 59,351)( 60,352)( 61,353)( 62,354)( 63,355)
( 64,356)( 65,357)( 66,358)( 67,359)( 68,360)( 69,361)( 70,362)( 71,363)
( 72,364)( 73,365)( 74,220)( 75,221)( 76,222)( 77,223)( 78,224)( 79,225)
( 80,226)( 81,227)( 82,228)( 83,229)( 84,230)( 85,231)( 86,232)( 87,233)
( 88,234)( 89,235)( 90,236)( 91,237)( 92,238)( 93,239)( 94,240)( 95,241)
( 96,242)( 97,243)( 98,244)( 99,245)(100,246)(101,247)(102,248)(103,249)
(104,250)(105,251)(106,252)(107,253)(108,254)(109,255)(110,256)(111,257)
(112,258)(113,259)(114,260)(115,261)(116,262)(117,263)(118,264)(119,265)
(120,266)(121,267)(122,268)(123,269)(124,270)(125,271)(126,272)(127,273)
(128,274)(129,275)(130,276)(131,277)(132,278)(133,279)(134,280)(135,281)
(136,282)(137,283)(138,284)(139,285)(140,286)(141,287)(142,288)(143,289)
(144,290)(145,291)(146,292)(147,366)(148,367)(149,368)(150,369)(151,370)
(152,371)(153,372)(154,373)(155,374)(156,375)(157,376)(158,377)(159,378)
(160,379)(161,380)(162,381)(163,382)(164,383)(165,384)(166,385)(167,386)
(168,387)(169,388)(170,389)(171,390)(172,391)(173,392)(174,393)(175,394)
(176,395)(177,396)(178,397)(179,398)(180,399)(181,400)(182,401)(183,402)
(184,403)(185,404)(186,405)(187,406)(188,407)(189,408)(190,409)(191,410)
(192,411)(193,412)(194,413)(195,414)(196,415)(197,416)(198,417)(199,418)
(200,419)(201,420)(202,421)(203,422)(204,423)(205,424)(206,425)(207,426)
(208,427)(209,428)(210,429)(211,430)(212,431)(213,432)(214,433)(215,434)
(216,435)(217,436)(218,437)(219,438);
poly := sub<Sym(438)|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*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 >;
References : None.
to this polytope