Polytope of Type {18,52}

Play with this polytope as a twisty puzzle

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

Twisty Puzzle