Polytope of Type {76,12}

Play with this polytope as a twisty puzzle

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.
Irregular Quotients (of which this is a minimal cover):
   None.

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

Twisty Puzzle