Polytope of Type {142,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {142,6}*1704
Also Known As : {142,6|2}. if this polytope has another name.
Group : SmallGroup(1704,34)
Rank : 3
Schlafli Type : {142,6}
Number of vertices, edges, etc : 142, 426, 6
Order of s0s1s2 : 426
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 : {142,2}*568
6-fold quotients : {71,2}*284
71-fold quotients : {2,6}*24
142-fold quotients : {2,3}*12
213-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 71)( 3, 70)( 4, 69)( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 64)
( 10, 63)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 58)( 16, 57)( 17, 56)
( 18, 55)( 19, 54)( 20, 53)( 21, 52)( 22, 51)( 23, 50)( 24, 49)( 25, 48)
( 26, 47)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 42)( 32, 41)( 33, 40)
( 34, 39)( 35, 38)( 36, 37)( 73,142)( 74,141)( 75,140)( 76,139)( 77,138)
( 78,137)( 79,136)( 80,135)( 81,134)( 82,133)( 83,132)( 84,131)( 85,130)
( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)( 91,124)( 92,123)( 93,122)
( 94,121)( 95,120)( 96,119)( 97,118)( 98,117)( 99,116)(100,115)(101,114)
(102,113)(103,112)(104,111)(105,110)(106,109)(107,108)(144,213)(145,212)
(146,211)(147,210)(148,209)(149,208)(150,207)(151,206)(152,205)(153,204)
(154,203)(155,202)(156,201)(157,200)(158,199)(159,198)(160,197)(161,196)
(162,195)(163,194)(164,193)(165,192)(166,191)(167,190)(168,189)(169,188)
(170,187)(171,186)(172,185)(173,184)(174,183)(175,182)(176,181)(177,180)
(178,179)(215,284)(216,283)(217,282)(218,281)(219,280)(220,279)(221,278)
(222,277)(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)(229,270)
(230,269)(231,268)(232,267)(233,266)(234,265)(235,264)(236,263)(237,262)
(238,261)(239,260)(240,259)(241,258)(242,257)(243,256)(244,255)(245,254)
(246,253)(247,252)(248,251)(249,250)(286,355)(287,354)(288,353)(289,352)
(290,351)(291,350)(292,349)(293,348)(294,347)(295,346)(296,345)(297,344)
(298,343)(299,342)(300,341)(301,340)(302,339)(303,338)(304,337)(305,336)
(306,335)(307,334)(308,333)(309,332)(310,331)(311,330)(312,329)(313,328)
(314,327)(315,326)(316,325)(317,324)(318,323)(319,322)(320,321)(357,426)
(358,425)(359,424)(360,423)(361,422)(362,421)(363,420)(364,419)(365,418)
(366,417)(367,416)(368,415)(369,414)(370,413)(371,412)(372,411)(373,410)
(374,409)(375,408)(376,407)(377,406)(378,405)(379,404)(380,403)(381,402)
(382,401)(383,400)(384,399)(385,398)(386,397)(387,396)(388,395)(389,394)
(390,393)(391,392);;
s1 := ( 1, 2)( 3, 71)( 4, 70)( 5, 69)( 6, 68)( 7, 67)( 8, 66)( 9, 65)
( 10, 64)( 11, 63)( 12, 62)( 13, 61)( 14, 60)( 15, 59)( 16, 58)( 17, 57)
( 18, 56)( 19, 55)( 20, 54)( 21, 53)( 22, 52)( 23, 51)( 24, 50)( 25, 49)
( 26, 48)( 27, 47)( 28, 46)( 29, 45)( 30, 44)( 31, 43)( 32, 42)( 33, 41)
( 34, 40)( 35, 39)( 36, 38)( 72,144)( 73,143)( 74,213)( 75,212)( 76,211)
( 77,210)( 78,209)( 79,208)( 80,207)( 81,206)( 82,205)( 83,204)( 84,203)
( 85,202)( 86,201)( 87,200)( 88,199)( 89,198)( 90,197)( 91,196)( 92,195)
( 93,194)( 94,193)( 95,192)( 96,191)( 97,190)( 98,189)( 99,188)(100,187)
(101,186)(102,185)(103,184)(104,183)(105,182)(106,181)(107,180)(108,179)
(109,178)(110,177)(111,176)(112,175)(113,174)(114,173)(115,172)(116,171)
(117,170)(118,169)(119,168)(120,167)(121,166)(122,165)(123,164)(124,163)
(125,162)(126,161)(127,160)(128,159)(129,158)(130,157)(131,156)(132,155)
(133,154)(134,153)(135,152)(136,151)(137,150)(138,149)(139,148)(140,147)
(141,146)(142,145)(214,215)(216,284)(217,283)(218,282)(219,281)(220,280)
(221,279)(222,278)(223,277)(224,276)(225,275)(226,274)(227,273)(228,272)
(229,271)(230,270)(231,269)(232,268)(233,267)(234,266)(235,265)(236,264)
(237,263)(238,262)(239,261)(240,260)(241,259)(242,258)(243,257)(244,256)
(245,255)(246,254)(247,253)(248,252)(249,251)(285,357)(286,356)(287,426)
(288,425)(289,424)(290,423)(291,422)(292,421)(293,420)(294,419)(295,418)
(296,417)(297,416)(298,415)(299,414)(300,413)(301,412)(302,411)(303,410)
(304,409)(305,408)(306,407)(307,406)(308,405)(309,404)(310,403)(311,402)
(312,401)(313,400)(314,399)(315,398)(316,397)(317,396)(318,395)(319,394)
(320,393)(321,392)(322,391)(323,390)(324,389)(325,388)(326,387)(327,386)
(328,385)(329,384)(330,383)(331,382)(332,381)(333,380)(334,379)(335,378)
(336,377)(337,376)(338,375)(339,374)(340,373)(341,372)(342,371)(343,370)
(344,369)(345,368)(346,367)(347,366)(348,365)(349,364)(350,363)(351,362)
(352,361)(353,360)(354,359)(355,358);;
s2 := ( 1,285)( 2,286)( 3,287)( 4,288)( 5,289)( 6,290)( 7,291)( 8,292)
( 9,293)( 10,294)( 11,295)( 12,296)( 13,297)( 14,298)( 15,299)( 16,300)
( 17,301)( 18,302)( 19,303)( 20,304)( 21,305)( 22,306)( 23,307)( 24,308)
( 25,309)( 26,310)( 27,311)( 28,312)( 29,313)( 30,314)( 31,315)( 32,316)
( 33,317)( 34,318)( 35,319)( 36,320)( 37,321)( 38,322)( 39,323)( 40,324)
( 41,325)( 42,326)( 43,327)( 44,328)( 45,329)( 46,330)( 47,331)( 48,332)
( 49,333)( 50,334)( 51,335)( 52,336)( 53,337)( 54,338)( 55,339)( 56,340)
( 57,341)( 58,342)( 59,343)( 60,344)( 61,345)( 62,346)( 63,347)( 64,348)
( 65,349)( 66,350)( 67,351)( 68,352)( 69,353)( 70,354)( 71,355)( 72,214)
( 73,215)( 74,216)( 75,217)( 76,218)( 77,219)( 78,220)( 79,221)( 80,222)
( 81,223)( 82,224)( 83,225)( 84,226)( 85,227)( 86,228)( 87,229)( 88,230)
( 89,231)( 90,232)( 91,233)( 92,234)( 93,235)( 94,236)( 95,237)( 96,238)
( 97,239)( 98,240)( 99,241)(100,242)(101,243)(102,244)(103,245)(104,246)
(105,247)(106,248)(107,249)(108,250)(109,251)(110,252)(111,253)(112,254)
(113,255)(114,256)(115,257)(116,258)(117,259)(118,260)(119,261)(120,262)
(121,263)(122,264)(123,265)(124,266)(125,267)(126,268)(127,269)(128,270)
(129,271)(130,272)(131,273)(132,274)(133,275)(134,276)(135,277)(136,278)
(137,279)(138,280)(139,281)(140,282)(141,283)(142,284)(143,356)(144,357)
(145,358)(146,359)(147,360)(148,361)(149,362)(150,363)(151,364)(152,365)
(153,366)(154,367)(155,368)(156,369)(157,370)(158,371)(159,372)(160,373)
(161,374)(162,375)(163,376)(164,377)(165,378)(166,379)(167,380)(168,381)
(169,382)(170,383)(171,384)(172,385)(173,386)(174,387)(175,388)(176,389)
(177,390)(178,391)(179,392)(180,393)(181,394)(182,395)(183,396)(184,397)
(185,398)(186,399)(187,400)(188,401)(189,402)(190,403)(191,404)(192,405)
(193,406)(194,407)(195,408)(196,409)(197,410)(198,411)(199,412)(200,413)
(201,414)(202,415)(203,416)(204,417)(205,418)(206,419)(207,420)(208,421)
(209,422)(210,423)(211,424)(212,425)(213,426);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(426)!( 2, 71)( 3, 70)( 4, 69)( 5, 68)( 6, 67)( 7, 66)( 8, 65)
( 9, 64)( 10, 63)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 58)( 16, 57)
( 17, 56)( 18, 55)( 19, 54)( 20, 53)( 21, 52)( 22, 51)( 23, 50)( 24, 49)
( 25, 48)( 26, 47)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 42)( 32, 41)
( 33, 40)( 34, 39)( 35, 38)( 36, 37)( 73,142)( 74,141)( 75,140)( 76,139)
( 77,138)( 78,137)( 79,136)( 80,135)( 81,134)( 82,133)( 83,132)( 84,131)
( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)( 91,124)( 92,123)
( 93,122)( 94,121)( 95,120)( 96,119)( 97,118)( 98,117)( 99,116)(100,115)
(101,114)(102,113)(103,112)(104,111)(105,110)(106,109)(107,108)(144,213)
(145,212)(146,211)(147,210)(148,209)(149,208)(150,207)(151,206)(152,205)
(153,204)(154,203)(155,202)(156,201)(157,200)(158,199)(159,198)(160,197)
(161,196)(162,195)(163,194)(164,193)(165,192)(166,191)(167,190)(168,189)
(169,188)(170,187)(171,186)(172,185)(173,184)(174,183)(175,182)(176,181)
(177,180)(178,179)(215,284)(216,283)(217,282)(218,281)(219,280)(220,279)
(221,278)(222,277)(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)
(229,270)(230,269)(231,268)(232,267)(233,266)(234,265)(235,264)(236,263)
(237,262)(238,261)(239,260)(240,259)(241,258)(242,257)(243,256)(244,255)
(245,254)(246,253)(247,252)(248,251)(249,250)(286,355)(287,354)(288,353)
(289,352)(290,351)(291,350)(292,349)(293,348)(294,347)(295,346)(296,345)
(297,344)(298,343)(299,342)(300,341)(301,340)(302,339)(303,338)(304,337)
(305,336)(306,335)(307,334)(308,333)(309,332)(310,331)(311,330)(312,329)
(313,328)(314,327)(315,326)(316,325)(317,324)(318,323)(319,322)(320,321)
(357,426)(358,425)(359,424)(360,423)(361,422)(362,421)(363,420)(364,419)
(365,418)(366,417)(367,416)(368,415)(369,414)(370,413)(371,412)(372,411)
(373,410)(374,409)(375,408)(376,407)(377,406)(378,405)(379,404)(380,403)
(381,402)(382,401)(383,400)(384,399)(385,398)(386,397)(387,396)(388,395)
(389,394)(390,393)(391,392);
s1 := Sym(426)!( 1, 2)( 3, 71)( 4, 70)( 5, 69)( 6, 68)( 7, 67)( 8, 66)
( 9, 65)( 10, 64)( 11, 63)( 12, 62)( 13, 61)( 14, 60)( 15, 59)( 16, 58)
( 17, 57)( 18, 56)( 19, 55)( 20, 54)( 21, 53)( 22, 52)( 23, 51)( 24, 50)
( 25, 49)( 26, 48)( 27, 47)( 28, 46)( 29, 45)( 30, 44)( 31, 43)( 32, 42)
( 33, 41)( 34, 40)( 35, 39)( 36, 38)( 72,144)( 73,143)( 74,213)( 75,212)
( 76,211)( 77,210)( 78,209)( 79,208)( 80,207)( 81,206)( 82,205)( 83,204)
( 84,203)( 85,202)( 86,201)( 87,200)( 88,199)( 89,198)( 90,197)( 91,196)
( 92,195)( 93,194)( 94,193)( 95,192)( 96,191)( 97,190)( 98,189)( 99,188)
(100,187)(101,186)(102,185)(103,184)(104,183)(105,182)(106,181)(107,180)
(108,179)(109,178)(110,177)(111,176)(112,175)(113,174)(114,173)(115,172)
(116,171)(117,170)(118,169)(119,168)(120,167)(121,166)(122,165)(123,164)
(124,163)(125,162)(126,161)(127,160)(128,159)(129,158)(130,157)(131,156)
(132,155)(133,154)(134,153)(135,152)(136,151)(137,150)(138,149)(139,148)
(140,147)(141,146)(142,145)(214,215)(216,284)(217,283)(218,282)(219,281)
(220,280)(221,279)(222,278)(223,277)(224,276)(225,275)(226,274)(227,273)
(228,272)(229,271)(230,270)(231,269)(232,268)(233,267)(234,266)(235,265)
(236,264)(237,263)(238,262)(239,261)(240,260)(241,259)(242,258)(243,257)
(244,256)(245,255)(246,254)(247,253)(248,252)(249,251)(285,357)(286,356)
(287,426)(288,425)(289,424)(290,423)(291,422)(292,421)(293,420)(294,419)
(295,418)(296,417)(297,416)(298,415)(299,414)(300,413)(301,412)(302,411)
(303,410)(304,409)(305,408)(306,407)(307,406)(308,405)(309,404)(310,403)
(311,402)(312,401)(313,400)(314,399)(315,398)(316,397)(317,396)(318,395)
(319,394)(320,393)(321,392)(322,391)(323,390)(324,389)(325,388)(326,387)
(327,386)(328,385)(329,384)(330,383)(331,382)(332,381)(333,380)(334,379)
(335,378)(336,377)(337,376)(338,375)(339,374)(340,373)(341,372)(342,371)
(343,370)(344,369)(345,368)(346,367)(347,366)(348,365)(349,364)(350,363)
(351,362)(352,361)(353,360)(354,359)(355,358);
s2 := Sym(426)!( 1,285)( 2,286)( 3,287)( 4,288)( 5,289)( 6,290)( 7,291)
( 8,292)( 9,293)( 10,294)( 11,295)( 12,296)( 13,297)( 14,298)( 15,299)
( 16,300)( 17,301)( 18,302)( 19,303)( 20,304)( 21,305)( 22,306)( 23,307)
( 24,308)( 25,309)( 26,310)( 27,311)( 28,312)( 29,313)( 30,314)( 31,315)
( 32,316)( 33,317)( 34,318)( 35,319)( 36,320)( 37,321)( 38,322)( 39,323)
( 40,324)( 41,325)( 42,326)( 43,327)( 44,328)( 45,329)( 46,330)( 47,331)
( 48,332)( 49,333)( 50,334)( 51,335)( 52,336)( 53,337)( 54,338)( 55,339)
( 56,340)( 57,341)( 58,342)( 59,343)( 60,344)( 61,345)( 62,346)( 63,347)
( 64,348)( 65,349)( 66,350)( 67,351)( 68,352)( 69,353)( 70,354)( 71,355)
( 72,214)( 73,215)( 74,216)( 75,217)( 76,218)( 77,219)( 78,220)( 79,221)
( 80,222)( 81,223)( 82,224)( 83,225)( 84,226)( 85,227)( 86,228)( 87,229)
( 88,230)( 89,231)( 90,232)( 91,233)( 92,234)( 93,235)( 94,236)( 95,237)
( 96,238)( 97,239)( 98,240)( 99,241)(100,242)(101,243)(102,244)(103,245)
(104,246)(105,247)(106,248)(107,249)(108,250)(109,251)(110,252)(111,253)
(112,254)(113,255)(114,256)(115,257)(116,258)(117,259)(118,260)(119,261)
(120,262)(121,263)(122,264)(123,265)(124,266)(125,267)(126,268)(127,269)
(128,270)(129,271)(130,272)(131,273)(132,274)(133,275)(134,276)(135,277)
(136,278)(137,279)(138,280)(139,281)(140,282)(141,283)(142,284)(143,356)
(144,357)(145,358)(146,359)(147,360)(148,361)(149,362)(150,363)(151,364)
(152,365)(153,366)(154,367)(155,368)(156,369)(157,370)(158,371)(159,372)
(160,373)(161,374)(162,375)(163,376)(164,377)(165,378)(166,379)(167,380)
(168,381)(169,382)(170,383)(171,384)(172,385)(173,386)(174,387)(175,388)
(176,389)(177,390)(178,391)(179,392)(180,393)(181,394)(182,395)(183,396)
(184,397)(185,398)(186,399)(187,400)(188,401)(189,402)(190,403)(191,404)
(192,405)(193,406)(194,407)(195,408)(196,409)(197,410)(198,411)(199,412)
(200,413)(201,414)(202,415)(203,416)(204,417)(205,418)(206,419)(207,420)
(208,421)(209,422)(210,423)(211,424)(212,425)(213,426);
poly := sub<Sym(426)|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 >;
References : None.
to this polytope