Polytope of Type {42,21}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {42,21}*1764
if this polytope has a name.
Group : SmallGroup(1764,211)
Rank : 3
Schlafli Type : {42,21}
Number of vertices, edges, etc : 42, 441, 21
Order of s0s1s2 : 42
Order of s0s1s2s1 : 42
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {14,21}*588
   7-fold quotients : {6,21}*252
   9-fold quotients : {14,7}*196
   21-fold quotients : {2,21}*84
   49-fold quotients : {6,3}*36
   63-fold quotients : {2,7}*28
   147-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

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

Twisty Puzzle