Polytope of Type {76,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {76,12}*1824
Also Known As : {76,12|2}. if this polytope has another name.
Group : SmallGroup(1824,620)
Rank : 3
Schlafli Type : {76,12}
Number of vertices, edges, etc : 76, 456, 12
Order of s0s1s2 : 228
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 : {38,12}*912, {76,6}*912a
3-fold quotients : {76,4}*608
4-fold quotients : {38,6}*456
6-fold quotients : {76,2}*304, {38,4}*304
12-fold quotients : {38,2}*152
19-fold quotients : {4,12}*96a
24-fold quotients : {19,2}*76
38-fold quotients : {2,12}*48, {4,6}*48a
57-fold quotients : {4,4}*32
76-fold quotients : {2,6}*24
114-fold quotients : {2,4}*16, {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)(116,133)(117,132)
(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(135,152)
(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)(143,144)
(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)
(162,163)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)
(180,183)(181,182)(192,209)(193,208)(194,207)(195,206)(196,205)(197,204)
(198,203)(199,202)(200,201)(211,228)(212,227)(213,226)(214,225)(215,224)
(216,223)(217,222)(218,221)(219,220)(229,286)(230,304)(231,303)(232,302)
(233,301)(234,300)(235,299)(236,298)(237,297)(238,296)(239,295)(240,294)
(241,293)(242,292)(243,291)(244,290)(245,289)(246,288)(247,287)(248,305)
(249,323)(250,322)(251,321)(252,320)(253,319)(254,318)(255,317)(256,316)
(257,315)(258,314)(259,313)(260,312)(261,311)(262,310)(263,309)(264,308)
(265,307)(266,306)(267,324)(268,342)(269,341)(270,340)(271,339)(272,338)
(273,337)(274,336)(275,335)(276,334)(277,333)(278,332)(279,331)(280,330)
(281,329)(282,328)(283,327)(284,326)(285,325)(343,400)(344,418)(345,417)
(346,416)(347,415)(348,414)(349,413)(350,412)(351,411)(352,410)(353,409)
(354,408)(355,407)(356,406)(357,405)(358,404)(359,403)(360,402)(361,401)
(362,419)(363,437)(364,436)(365,435)(366,434)(367,433)(368,432)(369,431)
(370,430)(371,429)(372,428)(373,427)(374,426)(375,425)(376,424)(377,423)
(378,422)(379,421)(380,420)(381,438)(382,456)(383,455)(384,454)(385,453)
(386,452)(387,451)(388,450)(389,449)(390,448)(391,447)(392,446)(393,445)
(394,444)(395,443)(396,442)(397,441)(398,440)(399,439);;
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)(115,344)(116,343)(117,361)(118,360)(119,359)(120,358)
(121,357)(122,356)(123,355)(124,354)(125,353)(126,352)(127,351)(128,350)
(129,349)(130,348)(131,347)(132,346)(133,345)(134,382)(135,381)(136,399)
(137,398)(138,397)(139,396)(140,395)(141,394)(142,393)(143,392)(144,391)
(145,390)(146,389)(147,388)(148,387)(149,386)(150,385)(151,384)(152,383)
(153,363)(154,362)(155,380)(156,379)(157,378)(158,377)(159,376)(160,375)
(161,374)(162,373)(163,372)(164,371)(165,370)(166,369)(167,368)(168,367)
(169,366)(170,365)(171,364)(172,401)(173,400)(174,418)(175,417)(176,416)
(177,415)(178,414)(179,413)(180,412)(181,411)(182,410)(183,409)(184,408)
(185,407)(186,406)(187,405)(188,404)(189,403)(190,402)(191,439)(192,438)
(193,456)(194,455)(195,454)(196,453)(197,452)(198,451)(199,450)(200,449)
(201,448)(202,447)(203,446)(204,445)(205,444)(206,443)(207,442)(208,441)
(209,440)(210,420)(211,419)(212,437)(213,436)(214,435)(215,434)(216,433)
(217,432)(218,431)(219,430)(220,429)(221,428)(222,427)(223,426)(224,425)
(225,424)(226,423)(227,422)(228,421);;
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)(229,362)(230,363)(231,364)(232,365)
(233,366)(234,367)(235,368)(236,369)(237,370)(238,371)(239,372)(240,373)
(241,374)(242,375)(243,376)(244,377)(245,378)(246,379)(247,380)(248,343)
(249,344)(250,345)(251,346)(252,347)(253,348)(254,349)(255,350)(256,351)
(257,352)(258,353)(259,354)(260,355)(261,356)(262,357)(263,358)(264,359)
(265,360)(266,361)(267,381)(268,382)(269,383)(270,384)(271,385)(272,386)
(273,387)(274,388)(275,389)(276,390)(277,391)(278,392)(279,393)(280,394)
(281,395)(282,396)(283,397)(284,398)(285,399)(286,419)(287,420)(288,421)
(289,422)(290,423)(291,424)(292,425)(293,426)(294,427)(295,428)(296,429)
(297,430)(298,431)(299,432)(300,433)(301,434)(302,435)(303,436)(304,437)
(305,400)(306,401)(307,402)(308,403)(309,404)(310,405)(311,406)(312,407)
(313,408)(314,409)(315,410)(316,411)(317,412)(318,413)(319,414)(320,415)
(321,416)(322,417)(323,418)(324,438)(325,439)(326,440)(327,441)(328,442)
(329,443)(330,444)(331,445)(332,446)(333,447)(334,448)(335,449)(336,450)
(337,451)(338,452)(339,453)(340,454)(341,455)(342,456);;
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*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 ];;
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)(116,133)
(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)
(135,152)(136,151)(137,150)(138,149)(139,148)(140,147)(141,146)(142,145)
(143,144)(154,171)(155,170)(156,169)(157,168)(158,167)(159,166)(160,165)
(161,164)(162,163)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)
(179,184)(180,183)(181,182)(192,209)(193,208)(194,207)(195,206)(196,205)
(197,204)(198,203)(199,202)(200,201)(211,228)(212,227)(213,226)(214,225)
(215,224)(216,223)(217,222)(218,221)(219,220)(229,286)(230,304)(231,303)
(232,302)(233,301)(234,300)(235,299)(236,298)(237,297)(238,296)(239,295)
(240,294)(241,293)(242,292)(243,291)(244,290)(245,289)(246,288)(247,287)
(248,305)(249,323)(250,322)(251,321)(252,320)(253,319)(254,318)(255,317)
(256,316)(257,315)(258,314)(259,313)(260,312)(261,311)(262,310)(263,309)
(264,308)(265,307)(266,306)(267,324)(268,342)(269,341)(270,340)(271,339)
(272,338)(273,337)(274,336)(275,335)(276,334)(277,333)(278,332)(279,331)
(280,330)(281,329)(282,328)(283,327)(284,326)(285,325)(343,400)(344,418)
(345,417)(346,416)(347,415)(348,414)(349,413)(350,412)(351,411)(352,410)
(353,409)(354,408)(355,407)(356,406)(357,405)(358,404)(359,403)(360,402)
(361,401)(362,419)(363,437)(364,436)(365,435)(366,434)(367,433)(368,432)
(369,431)(370,430)(371,429)(372,428)(373,427)(374,426)(375,425)(376,424)
(377,423)(378,422)(379,421)(380,420)(381,438)(382,456)(383,455)(384,454)
(385,453)(386,452)(387,451)(388,450)(389,449)(390,448)(391,447)(392,446)
(393,445)(394,444)(395,443)(396,442)(397,441)(398,440)(399,439);
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)(115,344)(116,343)(117,361)(118,360)(119,359)
(120,358)(121,357)(122,356)(123,355)(124,354)(125,353)(126,352)(127,351)
(128,350)(129,349)(130,348)(131,347)(132,346)(133,345)(134,382)(135,381)
(136,399)(137,398)(138,397)(139,396)(140,395)(141,394)(142,393)(143,392)
(144,391)(145,390)(146,389)(147,388)(148,387)(149,386)(150,385)(151,384)
(152,383)(153,363)(154,362)(155,380)(156,379)(157,378)(158,377)(159,376)
(160,375)(161,374)(162,373)(163,372)(164,371)(165,370)(166,369)(167,368)
(168,367)(169,366)(170,365)(171,364)(172,401)(173,400)(174,418)(175,417)
(176,416)(177,415)(178,414)(179,413)(180,412)(181,411)(182,410)(183,409)
(184,408)(185,407)(186,406)(187,405)(188,404)(189,403)(190,402)(191,439)
(192,438)(193,456)(194,455)(195,454)(196,453)(197,452)(198,451)(199,450)
(200,449)(201,448)(202,447)(203,446)(204,445)(205,444)(206,443)(207,442)
(208,441)(209,440)(210,420)(211,419)(212,437)(213,436)(214,435)(215,434)
(216,433)(217,432)(218,431)(219,430)(220,429)(221,428)(222,427)(223,426)
(224,425)(225,424)(226,423)(227,422)(228,421);
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)(229,362)(230,363)(231,364)
(232,365)(233,366)(234,367)(235,368)(236,369)(237,370)(238,371)(239,372)
(240,373)(241,374)(242,375)(243,376)(244,377)(245,378)(246,379)(247,380)
(248,343)(249,344)(250,345)(251,346)(252,347)(253,348)(254,349)(255,350)
(256,351)(257,352)(258,353)(259,354)(260,355)(261,356)(262,357)(263,358)
(264,359)(265,360)(266,361)(267,381)(268,382)(269,383)(270,384)(271,385)
(272,386)(273,387)(274,388)(275,389)(276,390)(277,391)(278,392)(279,393)
(280,394)(281,395)(282,396)(283,397)(284,398)(285,399)(286,419)(287,420)
(288,421)(289,422)(290,423)(291,424)(292,425)(293,426)(294,427)(295,428)
(296,429)(297,430)(298,431)(299,432)(300,433)(301,434)(302,435)(303,436)
(304,437)(305,400)(306,401)(307,402)(308,403)(309,404)(310,405)(311,406)
(312,407)(313,408)(314,409)(315,410)(316,411)(317,412)(318,413)(319,414)
(320,415)(321,416)(322,417)(323,418)(324,438)(325,439)(326,440)(327,441)
(328,442)(329,443)(330,444)(331,445)(332,446)(333,447)(334,448)(335,449)
(336,450)(337,451)(338,452)(339,453)(340,454)(341,455)(342,456);
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*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 >;
References : None.
to this polytope