Polytope of Type {152,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {152,6}*1824
Also Known As : {152,6|2}. if this polytope has another name.
Group : SmallGroup(1824,397)
Rank : 3
Schlafli Type : {152,6}
Number of vertices, edges, etc : 152, 456, 6
Order of s₀s₁s₂ : 456
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 : {76,6}*912a
   3-fold quotients : {152,2}*608
   4-fold quotients : {38,6}*456
   6-fold quotients : {76,2}*304
   12-fold quotients : {38,2}*152
   19-fold quotients : {8,6}*96
   24-fold quotients : {19,2}*76
   38-fold quotients : {4,6}*48a
   57-fold quotients : {8,2}*32
   76-fold quotients : {2,6}*24
   114-fold quotients : {4,2}*16
   152-fold quotients : {2,3}*12
   228-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)(  9, 12)
( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)( 45, 52)
( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)
( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 78, 95)( 79, 94)( 80, 93)( 81, 92)
( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 97,114)( 98,113)( 99,112)
(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(115,172)(116,190)
(117,189)(118,188)(119,187)(120,186)(121,185)(122,184)(123,183)(124,182)
(125,181)(126,180)(127,179)(128,178)(129,177)(130,176)(131,175)(132,174)
(133,173)(134,191)(135,209)(136,208)(137,207)(138,206)(139,205)(140,204)
(141,203)(142,202)(143,201)(144,200)(145,199)(146,198)(147,197)(148,196)
(149,195)(150,194)(151,193)(152,192)(153,210)(154,228)(155,227)(156,226)
(157,225)(158,224)(159,223)(160,222)(161,221)(162,220)(163,219)(164,218)
(165,217)(166,216)(167,215)(168,214)(169,213)(170,212)(171,211)(229,343)
(230,361)(231,360)(232,359)(233,358)(234,357)(235,356)(236,355)(237,354)
(238,353)(239,352)(240,351)(241,350)(242,349)(243,348)(244,347)(245,346)
(246,345)(247,344)(248,362)(249,380)(250,379)(251,378)(252,377)(253,376)
(254,375)(255,374)(256,373)(257,372)(258,371)(259,370)(260,369)(261,368)
(262,367)(263,366)(264,365)(265,364)(266,363)(267,381)(268,399)(269,398)
(270,397)(271,396)(272,395)(273,394)(274,393)(275,392)(276,391)(277,390)
(278,389)(279,388)(280,387)(281,386)(282,385)(283,384)(284,383)(285,382)
(286,400)(287,418)(288,417)(289,416)(290,415)(291,414)(292,413)(293,412)
(294,411)(295,410)(296,409)(297,408)(298,407)(299,406)(300,405)(301,404)
(302,403)(303,402)(304,401)(305,419)(306,437)(307,436)(308,435)(309,434)
(310,433)(311,432)(312,431)(313,430)(314,429)(315,428)(316,427)(317,426)
(318,425)(319,424)(320,423)(321,422)(322,421)(323,420)(324,438)(325,456)
(326,455)(327,454)(328,453)(329,452)(330,451)(331,450)(332,449)(333,448)
(334,447)(335,446)(336,445)(337,444)(338,443)(339,442)(340,441)(341,440)
(342,439);;
s1 := (  1,230)(  2,229)(  3,247)(  4,246)(  5,245)(  6,244)(  7,243)(  8,242)
(  9,241)( 10,240)( 11,239)( 12,238)( 13,237)( 14,236)( 15,235)( 16,234)
( 17,233)( 18,232)( 19,231)( 20,268)( 21,267)( 22,285)( 23,284)( 24,283)
( 25,282)( 26,281)( 27,280)( 28,279)( 29,278)( 30,277)( 31,276)( 32,275)
( 33,274)( 34,273)( 35,272)( 36,271)( 37,270)( 38,269)( 39,249)( 40,248)
( 41,266)( 42,265)( 43,264)( 44,263)( 45,262)( 46,261)( 47,260)( 48,259)
( 49,258)( 50,257)( 51,256)( 52,255)( 53,254)( 54,253)( 55,252)( 56,251)
( 57,250)( 58,287)( 59,286)( 60,304)( 61,303)( 62,302)( 63,301)( 64,300)
( 65,299)( 66,298)( 67,297)( 68,296)( 69,295)( 70,294)( 71,293)( 72,292)
( 73,291)( 74,290)( 75,289)( 76,288)( 77,325)( 78,324)( 79,342)( 80,341)
( 81,340)( 82,339)( 83,338)( 84,337)( 85,336)( 86,335)( 87,334)( 88,333)
( 89,332)( 90,331)( 91,330)( 92,329)( 93,328)( 94,327)( 95,326)( 96,306)
( 97,305)( 98,323)( 99,322)(100,321)(101,320)(102,319)(103,318)(104,317)
(105,316)(106,315)(107,314)(108,313)(109,312)(110,311)(111,310)(112,309)
(113,308)(114,307)(115,401)(116,400)(117,418)(118,417)(119,416)(120,415)
(121,414)(122,413)(123,412)(124,411)(125,410)(126,409)(127,408)(128,407)
(129,406)(130,405)(131,404)(132,403)(133,402)(134,439)(135,438)(136,456)
(137,455)(138,454)(139,453)(140,452)(141,451)(142,450)(143,449)(144,448)
(145,447)(146,446)(147,445)(148,444)(149,443)(150,442)(151,441)(152,440)
(153,420)(154,419)(155,437)(156,436)(157,435)(158,434)(159,433)(160,432)
(161,431)(162,430)(163,429)(164,428)(165,427)(166,426)(167,425)(168,424)
(169,423)(170,422)(171,421)(172,344)(173,343)(174,361)(175,360)(176,359)
(177,358)(178,357)(179,356)(180,355)(181,354)(182,353)(183,352)(184,351)
(185,350)(186,349)(187,348)(188,347)(189,346)(190,345)(191,382)(192,381)
(193,399)(194,398)(195,397)(196,396)(197,395)(198,394)(199,393)(200,392)
(201,391)(202,390)(203,389)(204,388)(205,387)(206,386)(207,385)(208,384)
(209,383)(210,363)(211,362)(212,380)(213,379)(214,378)(215,377)(216,376)
(217,375)(218,374)(219,373)(220,372)(221,371)(222,370)(223,369)(224,368)
(225,367)(226,366)(227,365)(228,364);;
s2 := (  1, 20)(  2, 21)(  3, 22)(  4, 23)(  5, 24)(  6, 25)(  7, 26)(  8, 27)
(  9, 28)( 10, 29)( 11, 30)( 12, 31)( 13, 32)( 14, 33)( 15, 34)( 16, 35)
( 17, 36)( 18, 37)( 19, 38)( 58, 77)( 59, 78)( 60, 79)( 61, 80)( 62, 81)
( 63, 82)( 64, 83)( 65, 84)( 66, 85)( 67, 86)( 68, 87)( 69, 88)( 70, 89)
( 71, 90)( 72, 91)( 73, 92)( 74, 93)( 75, 94)( 76, 95)(115,134)(116,135)
(117,136)(118,137)(119,138)(120,139)(121,140)(122,141)(123,142)(124,143)
(125,144)(126,145)(127,146)(128,147)(129,148)(130,149)(131,150)(132,151)
(133,152)(172,191)(173,192)(174,193)(175,194)(176,195)(177,196)(178,197)
(179,198)(180,199)(181,200)(182,201)(183,202)(184,203)(185,204)(186,205)
(187,206)(188,207)(189,208)(190,209)(229,248)(230,249)(231,250)(232,251)
(233,252)(234,253)(235,254)(236,255)(237,256)(238,257)(239,258)(240,259)
(241,260)(242,261)(243,262)(244,263)(245,264)(246,265)(247,266)(286,305)
(287,306)(288,307)(289,308)(290,309)(291,310)(292,311)(293,312)(294,313)
(295,314)(296,315)(297,316)(298,317)(299,318)(300,319)(301,320)(302,321)
(303,322)(304,323)(343,362)(344,363)(345,364)(346,365)(347,366)(348,367)
(349,368)(350,369)(351,370)(352,371)(353,372)(354,373)(355,374)(356,375)
(357,376)(358,377)(359,378)(360,379)(361,380)(400,419)(401,420)(402,421)
(403,422)(404,423)(405,424)(406,425)(407,426)(408,427)(409,428)(410,429)
(411,430)(412,431)(413,432)(414,433)(415,434)(416,435)(417,436)(418,437);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(456)!(  2, 19)(  3, 18)(  4, 17)(  5, 16)(  6, 15)(  7, 14)(  8, 13)
(  9, 12)( 10, 11)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)
( 27, 32)( 28, 31)( 29, 30)( 40, 57)( 41, 56)( 42, 55)( 43, 54)( 44, 53)
( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 59, 76)( 60, 75)( 61, 74)( 62, 73)
( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 78, 95)( 79, 94)( 80, 93)
( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)( 86, 87)( 97,114)( 98,113)
( 99,112)(100,111)(101,110)(102,109)(103,108)(104,107)(105,106)(115,172)
(116,190)(117,189)(118,188)(119,187)(120,186)(121,185)(122,184)(123,183)
(124,182)(125,181)(126,180)(127,179)(128,178)(129,177)(130,176)(131,175)
(132,174)(133,173)(134,191)(135,209)(136,208)(137,207)(138,206)(139,205)
(140,204)(141,203)(142,202)(143,201)(144,200)(145,199)(146,198)(147,197)
(148,196)(149,195)(150,194)(151,193)(152,192)(153,210)(154,228)(155,227)
(156,226)(157,225)(158,224)(159,223)(160,222)(161,221)(162,220)(163,219)
(164,218)(165,217)(166,216)(167,215)(168,214)(169,213)(170,212)(171,211)
(229,343)(230,361)(231,360)(232,359)(233,358)(234,357)(235,356)(236,355)
(237,354)(238,353)(239,352)(240,351)(241,350)(242,349)(243,348)(244,347)
(245,346)(246,345)(247,344)(248,362)(249,380)(250,379)(251,378)(252,377)
(253,376)(254,375)(255,374)(256,373)(257,372)(258,371)(259,370)(260,369)
(261,368)(262,367)(263,366)(264,365)(265,364)(266,363)(267,381)(268,399)
(269,398)(270,397)(271,396)(272,395)(273,394)(274,393)(275,392)(276,391)
(277,390)(278,389)(279,388)(280,387)(281,386)(282,385)(283,384)(284,383)
(285,382)(286,400)(287,418)(288,417)(289,416)(290,415)(291,414)(292,413)
(293,412)(294,411)(295,410)(296,409)(297,408)(298,407)(299,406)(300,405)
(301,404)(302,403)(303,402)(304,401)(305,419)(306,437)(307,436)(308,435)
(309,434)(310,433)(311,432)(312,431)(313,430)(314,429)(315,428)(316,427)
(317,426)(318,425)(319,424)(320,423)(321,422)(322,421)(323,420)(324,438)
(325,456)(326,455)(327,454)(328,453)(329,452)(330,451)(331,450)(332,449)
(333,448)(334,447)(335,446)(336,445)(337,444)(338,443)(339,442)(340,441)
(341,440)(342,439);
s1 := Sym(456)!(  1,230)(  2,229)(  3,247)(  4,246)(  5,245)(  6,244)(  7,243)
(  8,242)(  9,241)( 10,240)( 11,239)( 12,238)( 13,237)( 14,236)( 15,235)
( 16,234)( 17,233)( 18,232)( 19,231)( 20,268)( 21,267)( 22,285)( 23,284)
( 24,283)( 25,282)( 26,281)( 27,280)( 28,279)( 29,278)( 30,277)( 31,276)
( 32,275)( 33,274)( 34,273)( 35,272)( 36,271)( 37,270)( 38,269)( 39,249)
( 40,248)( 41,266)( 42,265)( 43,264)( 44,263)( 45,262)( 46,261)( 47,260)
( 48,259)( 49,258)( 50,257)( 51,256)( 52,255)( 53,254)( 54,253)( 55,252)
( 56,251)( 57,250)( 58,287)( 59,286)( 60,304)( 61,303)( 62,302)( 63,301)
( 64,300)( 65,299)( 66,298)( 67,297)( 68,296)( 69,295)( 70,294)( 71,293)
( 72,292)( 73,291)( 74,290)( 75,289)( 76,288)( 77,325)( 78,324)( 79,342)
( 80,341)( 81,340)( 82,339)( 83,338)( 84,337)( 85,336)( 86,335)( 87,334)
( 88,333)( 89,332)( 90,331)( 91,330)( 92,329)( 93,328)( 94,327)( 95,326)
( 96,306)( 97,305)( 98,323)( 99,322)(100,321)(101,320)(102,319)(103,318)
(104,317)(105,316)(106,315)(107,314)(108,313)(109,312)(110,311)(111,310)
(112,309)(113,308)(114,307)(115,401)(116,400)(117,418)(118,417)(119,416)
(120,415)(121,414)(122,413)(123,412)(124,411)(125,410)(126,409)(127,408)
(128,407)(129,406)(130,405)(131,404)(132,403)(133,402)(134,439)(135,438)
(136,456)(137,455)(138,454)(139,453)(140,452)(141,451)(142,450)(143,449)
(144,448)(145,447)(146,446)(147,445)(148,444)(149,443)(150,442)(151,441)
(152,440)(153,420)(154,419)(155,437)(156,436)(157,435)(158,434)(159,433)
(160,432)(161,431)(162,430)(163,429)(164,428)(165,427)(166,426)(167,425)
(168,424)(169,423)(170,422)(171,421)(172,344)(173,343)(174,361)(175,360)
(176,359)(177,358)(178,357)(179,356)(180,355)(181,354)(182,353)(183,352)
(184,351)(185,350)(186,349)(187,348)(188,347)(189,346)(190,345)(191,382)
(192,381)(193,399)(194,398)(195,397)(196,396)(197,395)(198,394)(199,393)
(200,392)(201,391)(202,390)(203,389)(204,388)(205,387)(206,386)(207,385)
(208,384)(209,383)(210,363)(211,362)(212,380)(213,379)(214,378)(215,377)
(216,376)(217,375)(218,374)(219,373)(220,372)(221,371)(222,370)(223,369)
(224,368)(225,367)(226,366)(227,365)(228,364);
s2 := Sym(456)!(  1, 20)(  2, 21)(  3, 22)(  4, 23)(  5, 24)(  6, 25)(  7, 26)
(  8, 27)(  9, 28)( 10, 29)( 11, 30)( 12, 31)( 13, 32)( 14, 33)( 15, 34)
( 16, 35)( 17, 36)( 18, 37)( 19, 38)( 58, 77)( 59, 78)( 60, 79)( 61, 80)
( 62, 81)( 63, 82)( 64, 83)( 65, 84)( 66, 85)( 67, 86)( 68, 87)( 69, 88)
( 70, 89)( 71, 90)( 72, 91)( 73, 92)( 74, 93)( 75, 94)( 76, 95)(115,134)
(116,135)(117,136)(118,137)(119,138)(120,139)(121,140)(122,141)(123,142)
(124,143)(125,144)(126,145)(127,146)(128,147)(129,148)(130,149)(131,150)
(132,151)(133,152)(172,191)(173,192)(174,193)(175,194)(176,195)(177,196)
(178,197)(179,198)(180,199)(181,200)(182,201)(183,202)(184,203)(185,204)
(186,205)(187,206)(188,207)(189,208)(190,209)(229,248)(230,249)(231,250)
(232,251)(233,252)(234,253)(235,254)(236,255)(237,256)(238,257)(239,258)
(240,259)(241,260)(242,261)(243,262)(244,263)(245,264)(246,265)(247,266)
(286,305)(287,306)(288,307)(289,308)(290,309)(291,310)(292,311)(293,312)
(294,313)(295,314)(296,315)(297,316)(298,317)(299,318)(300,319)(301,320)
(302,321)(303,322)(304,323)(343,362)(344,363)(345,364)(346,365)(347,366)
(348,367)(349,368)(350,369)(351,370)(352,371)(353,372)(354,373)(355,374)
(356,375)(357,376)(358,377)(359,378)(360,379)(361,380)(400,419)(401,420)
(402,421)(403,422)(404,423)(405,424)(406,425)(407,426)(408,427)(409,428)
(410,429)(411,430)(412,431)(413,432)(414,433)(415,434)(416,435)(417,436)
(418,437);
poly := sub<Sym(456)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope