Polytope of Type {14,9}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,9}*1764
if this polytope has a name.
Group : SmallGroup(1764,66)
Rank : 3
Schlafli Type : {14,9}
Number of vertices, edges, etc : 98, 441, 63
Order of s0s1s2 : 18
Order of s0s1s2s1 : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {14,3}*588
   49-fold quotients : {2,9}*36
   147-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 7.
      9 facets:
         9 of {14}*28
      14 vertex figures:
         14 of {9}*18
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 7.
      9 facets:
         9 of {14}*28
      14 vertex figures:
         14 of {9}*18
   P/N, where N=<s0*s1*s0*s1> of order 7.
      27 facets:
         21 of {2}*4
         6 of {14}*28
      14 vertex figures:
         14 of {9}*18

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

Twisty Puzzle