Polytope of Type {4,234}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,234}*1872a
Also Known As : {4,234|2}. if this polytope has another name.
Group : SmallGroup(1872,238)
Rank : 3
Schlafli Type : {4,234}
Number of vertices, edges, etc : 4, 468, 234
Order of s0s1s2 : 468
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 : {2,234}*936
   3-fold quotients : {4,78}*624a
   4-fold quotients : {2,117}*468
   6-fold quotients : {2,78}*312
   9-fold quotients : {4,26}*208
   12-fold quotients : {2,39}*156
   13-fold quotients : {4,18}*144a
   18-fold quotients : {2,26}*104
   26-fold quotients : {2,18}*72
   36-fold quotients : {2,13}*52
   39-fold quotients : {4,6}*48a
   52-fold quotients : {2,9}*36
   78-fold quotients : {2,6}*24
   117-fold quotients : {4,2}*16
   156-fold quotients : {2,3}*12
   234-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 := (235,352)(236,353)(237,354)(238,355)(239,356)(240,357)(241,358)(242,359)(243,360)(244,361)(245,362)(246,363)(247,364)(248,365)(249,366)(250,367)(251,368)(252,369)(253,370)(254,371)(255,372)(256,373)(257,374)(258,375)(259,376)(260,377)(261,378)(262,379)(263,380)(264,381)(265,382)(266,383)(267,384)(268,385)(269,386)(270,387)(271,388)(272,389)(273,390)(274,391)(275,392)(276,393)(277,394)(278,395)(279,396)(280,397)(281,398)(282,399)(283,400)(284,401)(285,402)(286,403)(287,404)(288,405)(289,406)(290,407)(291,408)(292,409)(293,410)(294,411)(295,412)(296,413)(297,414)(298,415)(299,416)(300,417)(301,418)(302,419)(303,420)(304,421)(305,422)(306,423)(307,424)(308,425)(309,426)(310,427)(311,428)(312,429)(313,430)(314,431)(315,432)(316,433)(317,434)(318,435)(319,436)(320,437)(321,438)(322,439)(323,440)(324,441)(325,442)(326,443)(327,444)(328,445)(329,446)(330,447)(331,448)(332,449)(333,450)(334,451)(335,452)(336,453)(337,454)(338,455)(339,456)(340,457)(341,458)(342,459)(343,460)(344,461)(345,462)(346,463)(347,464)(348,465)(349,466)(350,467)(351,468);;
s1 := (  1,235)(  2,237)(  3,236)(  4,271)(  5,273)(  6,272)(  7,268)(  8,270)(  9,269)( 10,265)( 11,267)( 12,266)( 13,262)( 14,264)( 15,263)( 16,259)( 17,261)( 18,260)( 19,256)( 20,258)( 21,257)( 22,253)( 23,255)( 24,254)( 25,250)( 26,252)( 27,251)( 28,247)( 29,249)( 30,248)( 31,244)( 32,246)( 33,245)( 34,241)( 35,243)( 36,242)( 37,238)( 38,240)( 39,239)( 40,315)( 41,314)( 42,313)( 43,351)( 44,350)( 45,349)( 46,348)( 47,347)( 48,346)( 49,345)( 50,344)( 51,343)( 52,342)( 53,341)( 54,340)( 55,339)( 56,338)( 57,337)( 58,336)( 59,335)( 60,334)( 61,333)( 62,332)( 63,331)( 64,330)( 65,329)( 66,328)( 67,327)( 68,326)( 69,325)( 70,324)( 71,323)( 72,322)( 73,321)( 74,320)( 75,319)( 76,318)( 77,317)( 78,316)( 79,276)( 80,275)( 81,274)( 82,312)( 83,311)( 84,310)( 85,309)( 86,308)( 87,307)( 88,306)( 89,305)( 90,304)( 91,303)( 92,302)( 93,301)( 94,300)( 95,299)( 96,298)( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,291)(104,290)(105,289)(106,288)(107,287)(108,286)(109,285)(110,284)(111,283)(112,282)(113,281)(114,280)(115,279)(116,278)(117,277)(118,352)(119,354)(120,353)(121,388)(122,390)(123,389)(124,385)(125,387)(126,386)(127,382)(128,384)(129,383)(130,379)(131,381)(132,380)(133,376)(134,378)(135,377)(136,373)(137,375)(138,374)(139,370)(140,372)(141,371)(142,367)(143,369)(144,368)(145,364)(146,366)(147,365)(148,361)(149,363)(150,362)(151,358)(152,360)(153,359)(154,355)(155,357)(156,356)(157,432)(158,431)(159,430)(160,468)(161,467)(162,466)(163,465)(164,464)(165,463)(166,462)(167,461)(168,460)(169,459)(170,458)(171,457)(172,456)(173,455)(174,454)(175,453)(176,452)(177,451)(178,450)(179,449)(180,448)(181,447)(182,446)(183,445)(184,444)(185,443)(186,442)(187,441)(188,440)(189,439)(190,438)(191,437)(192,436)(193,435)(194,434)(195,433)(196,393)(197,392)(198,391)(199,429)(200,428)(201,427)(202,426)(203,425)(204,424)(205,423)(206,422)(207,421)(208,420)(209,419)(210,418)(211,417)(212,416)(213,415)(214,414)(215,413)(216,412)(217,411)(218,410)(219,409)(220,408)(221,407)(222,406)(223,405)(224,404)(225,403)(226,402)(227,401)(228,400)(229,399)(230,398)(231,397)(232,396)(233,395)(234,394);;
s2 := (  1, 43)(  2, 45)(  3, 44)(  4, 40)(  5, 42)(  6, 41)(  7, 76)(  8, 78)(  9, 77)( 10, 73)( 11, 75)( 12, 74)( 13, 70)( 14, 72)( 15, 71)( 16, 67)( 17, 69)( 18, 68)( 19, 64)( 20, 66)( 21, 65)( 22, 61)( 23, 63)( 24, 62)( 25, 58)( 26, 60)( 27, 59)( 28, 55)( 29, 57)( 30, 56)( 31, 52)( 32, 54)( 33, 53)( 34, 49)( 35, 51)( 36, 50)( 37, 46)( 38, 48)( 39, 47)( 79, 84)( 80, 83)( 81, 82)( 85,117)( 86,116)( 87,115)( 88,114)( 89,113)( 90,112)( 91,111)( 92,110)( 93,109)( 94,108)( 95,107)( 96,106)( 97,105)( 98,104)( 99,103)(100,102)(118,160)(119,162)(120,161)(121,157)(122,159)(123,158)(124,193)(125,195)(126,194)(127,190)(128,192)(129,191)(130,187)(131,189)(132,188)(133,184)(134,186)(135,185)(136,181)(137,183)(138,182)(139,178)(140,180)(141,179)(142,175)(143,177)(144,176)(145,172)(146,174)(147,173)(148,169)(149,171)(150,170)(151,166)(152,168)(153,167)(154,163)(155,165)(156,164)(196,201)(197,200)(198,199)(202,234)(203,233)(204,232)(205,231)(206,230)(207,229)(208,228)(209,227)(210,226)(211,225)(212,224)(213,223)(214,222)(215,221)(216,220)(217,219)(235,277)(236,279)(237,278)(238,274)(239,276)(240,275)(241,310)(242,312)(243,311)(244,307)(245,309)(246,308)(247,304)(248,306)(249,305)(250,301)(251,303)(252,302)(253,298)(254,300)(255,299)(256,295)(257,297)(258,296)(259,292)(260,294)(261,293)(262,289)(263,291)(264,290)(265,286)(266,288)(267,287)(268,283)(269,285)(270,284)(271,280)(272,282)(273,281)(313,318)(314,317)(315,316)(319,351)(320,350)(321,349)(322,348)(323,347)(324,346)(325,345)(326,344)(327,343)(328,342)(329,341)(330,340)(331,339)(332,338)(333,337)(334,336)(352,394)(353,396)(354,395)(355,391)(356,393)(357,392)(358,427)(359,429)(360,428)(361,424)(362,426)(363,425)(364,421)(365,423)(366,422)(367,418)(368,420)(369,419)(370,415)(371,417)(372,416)(373,412)(374,414)(375,413)(376,409)(377,411)(378,410)(379,406)(380,408)(381,407)(382,403)(383,405)(384,404)(385,400)(386,402)(387,401)(388,397)(389,399)(390,398)(430,435)(431,434)(432,433)(436,468)(437,467)(438,466)(439,465)(440,464)(441,463)(442,462)(443,461)(444,460)(445,459)(446,458)(447,457)(448,456)(449,455)(450,454)(451,453);;
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*s0*s1*s0*s1*s0*s1, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(468)!(235,352)(236,353)(237,354)(238,355)(239,356)(240,357)(241,358)(242,359)(243,360)(244,361)(245,362)(246,363)(247,364)(248,365)(249,366)(250,367)(251,368)(252,369)(253,370)(254,371)(255,372)(256,373)(257,374)(258,375)(259,376)(260,377)(261,378)(262,379)(263,380)(264,381)(265,382)(266,383)(267,384)(268,385)(269,386)(270,387)(271,388)(272,389)(273,390)(274,391)(275,392)(276,393)(277,394)(278,395)(279,396)(280,397)(281,398)(282,399)(283,400)(284,401)(285,402)(286,403)(287,404)(288,405)(289,406)(290,407)(291,408)(292,409)(293,410)(294,411)(295,412)(296,413)(297,414)(298,415)(299,416)(300,417)(301,418)(302,419)(303,420)(304,421)(305,422)(306,423)(307,424)(308,425)(309,426)(310,427)(311,428)(312,429)(313,430)(314,431)(315,432)(316,433)(317,434)(318,435)(319,436)(320,437)(321,438)(322,439)(323,440)(324,441)(325,442)(326,443)(327,444)(328,445)(329,446)(330,447)(331,448)(332,449)(333,450)(334,451)(335,452)(336,453)(337,454)(338,455)(339,456)(340,457)(341,458)(342,459)(343,460)(344,461)(345,462)(346,463)(347,464)(348,465)(349,466)(350,467)(351,468);
s1 := Sym(468)!(  1,235)(  2,237)(  3,236)(  4,271)(  5,273)(  6,272)(  7,268)(  8,270)(  9,269)( 10,265)( 11,267)( 12,266)( 13,262)( 14,264)( 15,263)( 16,259)( 17,261)( 18,260)( 19,256)( 20,258)( 21,257)( 22,253)( 23,255)( 24,254)( 25,250)( 26,252)( 27,251)( 28,247)( 29,249)( 30,248)( 31,244)( 32,246)( 33,245)( 34,241)( 35,243)( 36,242)( 37,238)( 38,240)( 39,239)( 40,315)( 41,314)( 42,313)( 43,351)( 44,350)( 45,349)( 46,348)( 47,347)( 48,346)( 49,345)( 50,344)( 51,343)( 52,342)( 53,341)( 54,340)( 55,339)( 56,338)( 57,337)( 58,336)( 59,335)( 60,334)( 61,333)( 62,332)( 63,331)( 64,330)( 65,329)( 66,328)( 67,327)( 68,326)( 69,325)( 70,324)( 71,323)( 72,322)( 73,321)( 74,320)( 75,319)( 76,318)( 77,317)( 78,316)( 79,276)( 80,275)( 81,274)( 82,312)( 83,311)( 84,310)( 85,309)( 86,308)( 87,307)( 88,306)( 89,305)( 90,304)( 91,303)( 92,302)( 93,301)( 94,300)( 95,299)( 96,298)( 97,297)( 98,296)( 99,295)(100,294)(101,293)(102,292)(103,291)(104,290)(105,289)(106,288)(107,287)(108,286)(109,285)(110,284)(111,283)(112,282)(113,281)(114,280)(115,279)(116,278)(117,277)(118,352)(119,354)(120,353)(121,388)(122,390)(123,389)(124,385)(125,387)(126,386)(127,382)(128,384)(129,383)(130,379)(131,381)(132,380)(133,376)(134,378)(135,377)(136,373)(137,375)(138,374)(139,370)(140,372)(141,371)(142,367)(143,369)(144,368)(145,364)(146,366)(147,365)(148,361)(149,363)(150,362)(151,358)(152,360)(153,359)(154,355)(155,357)(156,356)(157,432)(158,431)(159,430)(160,468)(161,467)(162,466)(163,465)(164,464)(165,463)(166,462)(167,461)(168,460)(169,459)(170,458)(171,457)(172,456)(173,455)(174,454)(175,453)(176,452)(177,451)(178,450)(179,449)(180,448)(181,447)(182,446)(183,445)(184,444)(185,443)(186,442)(187,441)(188,440)(189,439)(190,438)(191,437)(192,436)(193,435)(194,434)(195,433)(196,393)(197,392)(198,391)(199,429)(200,428)(201,427)(202,426)(203,425)(204,424)(205,423)(206,422)(207,421)(208,420)(209,419)(210,418)(211,417)(212,416)(213,415)(214,414)(215,413)(216,412)(217,411)(218,410)(219,409)(220,408)(221,407)(222,406)(223,405)(224,404)(225,403)(226,402)(227,401)(228,400)(229,399)(230,398)(231,397)(232,396)(233,395)(234,394);
s2 := Sym(468)!(  1, 43)(  2, 45)(  3, 44)(  4, 40)(  5, 42)(  6, 41)(  7, 76)(  8, 78)(  9, 77)( 10, 73)( 11, 75)( 12, 74)( 13, 70)( 14, 72)( 15, 71)( 16, 67)( 17, 69)( 18, 68)( 19, 64)( 20, 66)( 21, 65)( 22, 61)( 23, 63)( 24, 62)( 25, 58)( 26, 60)( 27, 59)( 28, 55)( 29, 57)( 30, 56)( 31, 52)( 32, 54)( 33, 53)( 34, 49)( 35, 51)( 36, 50)( 37, 46)( 38, 48)( 39, 47)( 79, 84)( 80, 83)( 81, 82)( 85,117)( 86,116)( 87,115)( 88,114)( 89,113)( 90,112)( 91,111)( 92,110)( 93,109)( 94,108)( 95,107)( 96,106)( 97,105)( 98,104)( 99,103)(100,102)(118,160)(119,162)(120,161)(121,157)(122,159)(123,158)(124,193)(125,195)(126,194)(127,190)(128,192)(129,191)(130,187)(131,189)(132,188)(133,184)(134,186)(135,185)(136,181)(137,183)(138,182)(139,178)(140,180)(141,179)(142,175)(143,177)(144,176)(145,172)(146,174)(147,173)(148,169)(149,171)(150,170)(151,166)(152,168)(153,167)(154,163)(155,165)(156,164)(196,201)(197,200)(198,199)(202,234)(203,233)(204,232)(205,231)(206,230)(207,229)(208,228)(209,227)(210,226)(211,225)(212,224)(213,223)(214,222)(215,221)(216,220)(217,219)(235,277)(236,279)(237,278)(238,274)(239,276)(240,275)(241,310)(242,312)(243,311)(244,307)(245,309)(246,308)(247,304)(248,306)(249,305)(250,301)(251,303)(252,302)(253,298)(254,300)(255,299)(256,295)(257,297)(258,296)(259,292)(260,294)(261,293)(262,289)(263,291)(264,290)(265,286)(266,288)(267,287)(268,283)(269,285)(270,284)(271,280)(272,282)(273,281)(313,318)(314,317)(315,316)(319,351)(320,350)(321,349)(322,348)(323,347)(324,346)(325,345)(326,344)(327,343)(328,342)(329,341)(330,340)(331,339)(332,338)(333,337)(334,336)(352,394)(353,396)(354,395)(355,391)(356,393)(357,392)(358,427)(359,429)(360,428)(361,424)(362,426)(363,425)(364,421)(365,423)(366,422)(367,418)(368,420)(369,419)(370,415)(371,417)(372,416)(373,412)(374,414)(375,413)(376,409)(377,411)(378,410)(379,406)(380,408)(381,407)(382,403)(383,405)(384,404)(385,400)(386,402)(387,401)(388,397)(389,399)(390,398)(430,435)(431,434)(432,433)(436,468)(437,467)(438,466)(439,465)(440,464)(441,463)(442,462)(443,461)(444,460)(445,459)(446,458)(447,457)(448,456)(449,455)(450,454)(451,453);
poly := sub<Sym(468)|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*s0*s1*s0*s1*s0*s1, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope

Twisty Puzzle