Polytope of Type {14,18}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,18}*1764
if this polytope has a name.
Group : SmallGroup(1764,66)
Rank : 3
Schlafli Type : {14,18}
Number of vertices, edges, etc : 49, 441, 63
Order of s₀s₁s₂ : 9
Order of s₀s₁s₂s₁ : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {14,6}*588
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)(  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, 15)(  3, 29)(  4, 43)(  5,  8)(  6, 22)(  7, 36)(  9, 19)( 10, 33)( 11, 47)( 13, 26)( 14, 40)( 17, 30)( 18, 44)( 20, 23)( 21, 37)( 24, 34)( 25, 48)( 28, 41)( 32, 45)( 35, 38)( 39, 49)( 50, 99)( 51,113)( 52,127)( 53,141)( 54,106)( 55,120)( 56,134)( 57,103)( 58,117)( 59,131)( 60,145)( 61,110)( 62,124)( 63,138)( 64,100)( 65,114)( 66,128)( 67,142)( 68,107)( 69,121)( 70,135)( 71,104)( 72,118)( 73,132)( 74,146)( 75,111)( 76,125)( 77,139)( 78,101)( 79,115)( 80,129)( 81,143)( 82,108)( 83,122)( 84,136)( 85,105)( 86,119)( 87,133)( 88,147)( 89,112)( 90,126)( 91,140)( 92,102)( 93,116)( 94,130)( 95,144)( 96,109)( 97,123)( 98,137)(148,393)(149,407)(150,421)(151,435)(152,400)(153,414)(154,428)(155,397)(156,411)(157,425)(158,439)(159,404)(160,418)(161,432)(162,394)(163,408)(164,422)(165,436)(166,401)(167,415)(168,429)(169,398)(170,412)(171,426)(172,440)(173,405)(174,419)(175,433)(176,395)(177,409)(178,423)(179,437)(180,402)(181,416)(182,430)(183,399)(184,413)(185,427)(186,441)(187,406)(188,420)(189,434)(190,396)(191,410)(192,424)(193,438)(194,403)(195,417)(196,431)(197,344)(198,358)(199,372)(200,386)(201,351)(202,365)(203,379)(204,348)(205,362)(206,376)(207,390)(208,355)(209,369)(210,383)(211,345)(212,359)(213,373)(214,387)(215,352)(216,366)(217,380)(218,349)(219,363)(220,377)(221,391)(222,356)(223,370)(224,384)(225,346)(226,360)(227,374)(228,388)(229,353)(230,367)(231,381)(232,350)(233,364)(234,378)(235,392)(236,357)(237,371)(238,385)(239,347)(240,361)(241,375)(242,389)(243,354)(244,368)(245,382)(246,295)(247,309)(248,323)(249,337)(250,302)(251,316)(252,330)(253,299)(254,313)(255,327)(256,341)(257,306)(258,320)(259,334)(260,296)(261,310)(262,324)(263,338)(264,303)(265,317)(266,331)(267,300)(268,314)(269,328)(270,342)(271,307)(272,321)(273,335)(274,297)(275,311)(276,325)(277,339)(278,304)(279,318)(280,332)(281,301)(282,315)(283,329)(284,343)(285,308)(286,322)(287,336)(288,298)(289,312)(290,326)(291,340)(292,305)(293,319)(294,333);;
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*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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, 15)(  3, 29)(  4, 43)(  5,  8)(  6, 22)(  7, 36)(  9, 19)( 10, 33)( 11, 47)( 13, 26)( 14, 40)( 17, 30)( 18, 44)( 20, 23)( 21, 37)( 24, 34)( 25, 48)( 28, 41)( 32, 45)( 35, 38)( 39, 49)( 50, 99)( 51,113)( 52,127)( 53,141)( 54,106)( 55,120)( 56,134)( 57,103)( 58,117)( 59,131)( 60,145)( 61,110)( 62,124)( 63,138)( 64,100)( 65,114)( 66,128)( 67,142)( 68,107)( 69,121)( 70,135)( 71,104)( 72,118)( 73,132)( 74,146)( 75,111)( 76,125)( 77,139)( 78,101)( 79,115)( 80,129)( 81,143)( 82,108)( 83,122)( 84,136)( 85,105)( 86,119)( 87,133)( 88,147)( 89,112)( 90,126)( 91,140)( 92,102)( 93,116)( 94,130)( 95,144)( 96,109)( 97,123)( 98,137)(148,393)(149,407)(150,421)(151,435)(152,400)(153,414)(154,428)(155,397)(156,411)(157,425)(158,439)(159,404)(160,418)(161,432)(162,394)(163,408)(164,422)(165,436)(166,401)(167,415)(168,429)(169,398)(170,412)(171,426)(172,440)(173,405)(174,419)(175,433)(176,395)(177,409)(178,423)(179,437)(180,402)(181,416)(182,430)(183,399)(184,413)(185,427)(186,441)(187,406)(188,420)(189,434)(190,396)(191,410)(192,424)(193,438)(194,403)(195,417)(196,431)(197,344)(198,358)(199,372)(200,386)(201,351)(202,365)(203,379)(204,348)(205,362)(206,376)(207,390)(208,355)(209,369)(210,383)(211,345)(212,359)(213,373)(214,387)(215,352)(216,366)(217,380)(218,349)(219,363)(220,377)(221,391)(222,356)(223,370)(224,384)(225,346)(226,360)(227,374)(228,388)(229,353)(230,367)(231,381)(232,350)(233,364)(234,378)(235,392)(236,357)(237,371)(238,385)(239,347)(240,361)(241,375)(242,389)(243,354)(244,368)(245,382)(246,295)(247,309)(248,323)(249,337)(250,302)(251,316)(252,330)(253,299)(254,313)(255,327)(256,341)(257,306)(258,320)(259,334)(260,296)(261,310)(262,324)(263,338)(264,303)(265,317)(266,331)(267,300)(268,314)(269,328)(270,342)(271,307)(272,321)(273,335)(274,297)(275,311)(276,325)(277,339)(278,304)(279,318)(280,332)(281,301)(282,315)(283,329)(284,343)(285,308)(286,322)(287,336)(288,298)(289,312)(290,326)(291,340)(292,305)(293,319)(294,333);
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*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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

Polytope of Type {14,18}

Twisty Puzzle