Polytope of Type {15,10}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,240046)
Rank : 3
Schlafli Type : {15,10}
Number of vertices, edges, etc : 96, 480, 64
Order of s0s1s2 : 24
Order of s0s1s2s1 : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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) :
   2-fold quotients : {15,10}*960
   3-fold quotients : {5,10}*640
   6-fold quotients : {5,5}*320, {5,10}*320a, {5,10}*320b
   12-fold quotients : {5,5}*160
   160-fold quotients : {3,2}*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*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1> of order 2.
      32 facets:
         32 of {15}*30
      48 vertex figures:
         48 of {10}*20

Permutation Representation (GAP) : 
s0 := (  5,  8)(  6,  7)(  9, 11)( 10, 12)( 13, 14)( 15, 16)( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 26)( 22, 25)( 23, 28)( 24, 27)( 33,129)( 34,130)( 35,131)( 36,132)( 37,136)( 38,135)( 39,134)( 40,133)( 41,139)( 42,140)( 43,137)( 44,138)( 45,142)( 46,141)( 47,144)( 48,143)( 49,160)( 50,159)( 51,158)( 52,157)( 53,154)( 54,153)( 55,156)( 56,155)( 57,150)( 58,149)( 59,152)( 60,151)( 61,148)( 62,147)( 63,146)( 64,145)( 65, 97)( 66, 98)( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)( 72,101)( 73,107)( 74,108)( 75,105)( 76,106)( 77,110)( 78,109)( 79,112)( 80,111)( 81,128)( 82,127)( 83,126)( 84,125)( 85,122)( 86,121)( 87,124)( 88,123)( 89,118)( 90,117)( 91,120)( 92,119)( 93,116)( 94,115)( 95,114)( 96,113)(161,321)(162,322)(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)(169,331)(170,332)(171,329)(172,330)(173,334)(174,333)(175,336)(176,335)(177,352)(178,351)(179,350)(180,349)(181,346)(182,345)(183,348)(184,347)(185,342)(186,341)(187,344)(188,343)(189,340)(190,339)(191,338)(192,337)(193,449)(194,450)(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)(201,459)(202,460)(203,457)(204,458)(205,462)(206,461)(207,464)(208,463)(209,480)(210,479)(211,478)(212,477)(213,474)(214,473)(215,476)(216,475)(217,470)(218,469)(219,472)(220,471)(221,468)(222,467)(223,466)(224,465)(225,417)(226,418)(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)(233,427)(234,428)(235,425)(236,426)(237,430)(238,429)(239,432)(240,431)(241,448)(242,447)(243,446)(244,445)(245,442)(246,441)(247,444)(248,443)(249,438)(250,437)(251,440)(252,439)(253,436)(254,435)(255,434)(256,433)(257,385)(258,386)(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,395)(266,396)(267,393)(268,394)(269,398)(270,397)(271,400)(272,399)(273,416)(274,415)(275,414)(276,413)(277,410)(278,409)(279,412)(280,411)(281,406)(282,405)(283,408)(284,407)(285,404)(286,403)(287,402)(288,401)(289,353)(290,354)(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,363)(298,364)(299,361)(300,362)(301,366)(302,365)(303,368)(304,367)(305,384)(306,383)(307,382)(308,381)(309,378)(310,377)(311,380)(312,379)(313,374)(314,373)(315,376)(316,375)(317,372)(318,371)(319,370)(320,369);;
s1 := (  1,193)(  2,194)(  3,212)(  4,211)(  5,213)(  6,214)(  7,200)(  8,199)(  9,224)( 10,223)( 11,205)( 12,206)( 13,203)( 14,204)( 15,218)( 16,217)( 17,210)( 18,209)( 19,196)( 20,195)( 21,197)( 22,198)( 23,215)( 24,216)( 25,208)( 26,207)( 27,222)( 28,221)( 29,220)( 30,219)( 31,202)( 32,201)( 33,161)( 34,162)( 35,180)( 36,179)( 37,181)( 38,182)( 39,168)( 40,167)( 41,192)( 42,191)( 43,173)( 44,174)( 45,171)( 46,172)( 47,186)( 48,185)( 49,178)( 50,177)( 51,164)( 52,163)( 53,165)( 54,166)( 55,183)( 56,184)( 57,176)( 58,175)( 59,190)( 60,189)( 61,188)( 62,187)( 63,170)( 64,169)( 65,289)( 66,290)( 67,308)( 68,307)( 69,309)( 70,310)( 71,296)( 72,295)( 73,320)( 74,319)( 75,301)( 76,302)( 77,299)( 78,300)( 79,314)( 80,313)( 81,306)( 82,305)( 83,292)( 84,291)( 85,293)( 86,294)( 87,311)( 88,312)( 89,304)( 90,303)( 91,318)( 92,317)( 93,316)( 94,315)( 95,298)( 96,297)( 97,257)( 98,258)( 99,276)(100,275)(101,277)(102,278)(103,264)(104,263)(105,288)(106,287)(107,269)(108,270)(109,267)(110,268)(111,282)(112,281)(113,274)(114,273)(115,260)(116,259)(117,261)(118,262)(119,279)(120,280)(121,272)(122,271)(123,286)(124,285)(125,284)(126,283)(127,266)(128,265)(129,225)(130,226)(131,244)(132,243)(133,245)(134,246)(135,232)(136,231)(137,256)(138,255)(139,237)(140,238)(141,235)(142,236)(143,250)(144,249)(145,242)(146,241)(147,228)(148,227)(149,229)(150,230)(151,247)(152,248)(153,240)(154,239)(155,254)(156,253)(157,252)(158,251)(159,234)(160,233)(321,353)(322,354)(323,372)(324,371)(325,373)(326,374)(327,360)(328,359)(329,384)(330,383)(331,365)(332,366)(333,363)(334,364)(335,378)(336,377)(337,370)(338,369)(339,356)(340,355)(341,357)(342,358)(343,375)(344,376)(345,368)(346,367)(347,382)(348,381)(349,380)(350,379)(351,362)(352,361)(385,449)(386,450)(387,468)(388,467)(389,469)(390,470)(391,456)(392,455)(393,480)(394,479)(395,461)(396,462)(397,459)(398,460)(399,474)(400,473)(401,466)(402,465)(403,452)(404,451)(405,453)(406,454)(407,471)(408,472)(409,464)(410,463)(411,478)(412,477)(413,476)(414,475)(415,458)(416,457)(419,436)(420,435)(421,437)(422,438)(423,424)(425,448)(426,447)(427,429)(428,430)(431,442)(432,441)(433,434)(443,446)(444,445);;
s2 := (  1,  3)(  2,  4)(  5,  6)(  7,  8)( 13, 16)( 14, 15)( 17, 30)( 18, 29)( 19, 32)( 20, 31)( 21, 28)( 22, 27)( 23, 26)( 24, 25)( 33,131)( 34,132)( 35,129)( 36,130)( 37,134)( 38,133)( 39,136)( 40,135)( 41,137)( 42,138)( 43,139)( 44,140)( 45,144)( 46,143)( 47,142)( 48,141)( 49,158)( 50,157)( 51,160)( 52,159)( 53,156)( 54,155)( 55,154)( 56,153)( 57,152)( 58,151)( 59,150)( 60,149)( 61,146)( 62,145)( 63,148)( 64,147)( 65, 99)( 66,100)( 67, 97)( 68, 98)( 69,102)( 70,101)( 71,104)( 72,103)( 73,105)( 74,106)( 75,107)( 76,108)( 77,112)( 78,111)( 79,110)( 80,109)( 81,126)( 82,125)( 83,128)( 84,127)( 85,124)( 86,123)( 87,122)( 88,121)( 89,120)( 90,119)( 91,118)( 92,117)( 93,114)( 94,113)( 95,116)( 96,115)(161,163)(162,164)(165,166)(167,168)(173,176)(174,175)(177,190)(178,189)(179,192)(180,191)(181,188)(182,187)(183,186)(184,185)(193,291)(194,292)(195,289)(196,290)(197,294)(198,293)(199,296)(200,295)(201,297)(202,298)(203,299)(204,300)(205,304)(206,303)(207,302)(208,301)(209,318)(210,317)(211,320)(212,319)(213,316)(214,315)(215,314)(216,313)(217,312)(218,311)(219,310)(220,309)(221,306)(222,305)(223,308)(224,307)(225,259)(226,260)(227,257)(228,258)(229,262)(230,261)(231,264)(232,263)(233,265)(234,266)(235,267)(236,268)(237,272)(238,271)(239,270)(240,269)(241,286)(242,285)(243,288)(244,287)(245,284)(246,283)(247,282)(248,281)(249,280)(250,279)(251,278)(252,277)(253,274)(254,273)(255,276)(256,275)(321,323)(322,324)(325,326)(327,328)(333,336)(334,335)(337,350)(338,349)(339,352)(340,351)(341,348)(342,347)(343,346)(344,345)(353,451)(354,452)(355,449)(356,450)(357,454)(358,453)(359,456)(360,455)(361,457)(362,458)(363,459)(364,460)(365,464)(366,463)(367,462)(368,461)(369,478)(370,477)(371,480)(372,479)(373,476)(374,475)(375,474)(376,473)(377,472)(378,471)(379,470)(380,469)(381,466)(382,465)(383,468)(384,467)(385,419)(386,420)(387,417)(388,418)(389,422)(390,421)(391,424)(392,423)(393,425)(394,426)(395,427)(396,428)(397,432)(398,431)(399,430)(400,429)(401,446)(402,445)(403,448)(404,447)(405,444)(406,443)(407,442)(408,441)(409,440)(410,439)(411,438)(412,437)(413,434)(414,433)(415,436)(416,435);;
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*s2*s1*s0*s1*s0*s1*s0*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, 
s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(480)!(  5,  8)(  6,  7)(  9, 11)( 10, 12)( 13, 14)( 15, 16)( 17, 32)( 18, 31)( 19, 30)( 20, 29)( 21, 26)( 22, 25)( 23, 28)( 24, 27)( 33,129)( 34,130)( 35,131)( 36,132)( 37,136)( 38,135)( 39,134)( 40,133)( 41,139)( 42,140)( 43,137)( 44,138)( 45,142)( 46,141)( 47,144)( 48,143)( 49,160)( 50,159)( 51,158)( 52,157)( 53,154)( 54,153)( 55,156)( 56,155)( 57,150)( 58,149)( 59,152)( 60,151)( 61,148)( 62,147)( 63,146)( 64,145)( 65, 97)( 66, 98)( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)( 72,101)( 73,107)( 74,108)( 75,105)( 76,106)( 77,110)( 78,109)( 79,112)( 80,111)( 81,128)( 82,127)( 83,126)( 84,125)( 85,122)( 86,121)( 87,124)( 88,123)( 89,118)( 90,117)( 91,120)( 92,119)( 93,116)( 94,115)( 95,114)( 96,113)(161,321)(162,322)(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)(169,331)(170,332)(171,329)(172,330)(173,334)(174,333)(175,336)(176,335)(177,352)(178,351)(179,350)(180,349)(181,346)(182,345)(183,348)(184,347)(185,342)(186,341)(187,344)(188,343)(189,340)(190,339)(191,338)(192,337)(193,449)(194,450)(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)(201,459)(202,460)(203,457)(204,458)(205,462)(206,461)(207,464)(208,463)(209,480)(210,479)(211,478)(212,477)(213,474)(214,473)(215,476)(216,475)(217,470)(218,469)(219,472)(220,471)(221,468)(222,467)(223,466)(224,465)(225,417)(226,418)(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)(233,427)(234,428)(235,425)(236,426)(237,430)(238,429)(239,432)(240,431)(241,448)(242,447)(243,446)(244,445)(245,442)(246,441)(247,444)(248,443)(249,438)(250,437)(251,440)(252,439)(253,436)(254,435)(255,434)(256,433)(257,385)(258,386)(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,395)(266,396)(267,393)(268,394)(269,398)(270,397)(271,400)(272,399)(273,416)(274,415)(275,414)(276,413)(277,410)(278,409)(279,412)(280,411)(281,406)(282,405)(283,408)(284,407)(285,404)(286,403)(287,402)(288,401)(289,353)(290,354)(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,363)(298,364)(299,361)(300,362)(301,366)(302,365)(303,368)(304,367)(305,384)(306,383)(307,382)(308,381)(309,378)(310,377)(311,380)(312,379)(313,374)(314,373)(315,376)(316,375)(317,372)(318,371)(319,370)(320,369);
s1 := Sym(480)!(  1,193)(  2,194)(  3,212)(  4,211)(  5,213)(  6,214)(  7,200)(  8,199)(  9,224)( 10,223)( 11,205)( 12,206)( 13,203)( 14,204)( 15,218)( 16,217)( 17,210)( 18,209)( 19,196)( 20,195)( 21,197)( 22,198)( 23,215)( 24,216)( 25,208)( 26,207)( 27,222)( 28,221)( 29,220)( 30,219)( 31,202)( 32,201)( 33,161)( 34,162)( 35,180)( 36,179)( 37,181)( 38,182)( 39,168)( 40,167)( 41,192)( 42,191)( 43,173)( 44,174)( 45,171)( 46,172)( 47,186)( 48,185)( 49,178)( 50,177)( 51,164)( 52,163)( 53,165)( 54,166)( 55,183)( 56,184)( 57,176)( 58,175)( 59,190)( 60,189)( 61,188)( 62,187)( 63,170)( 64,169)( 65,289)( 66,290)( 67,308)( 68,307)( 69,309)( 70,310)( 71,296)( 72,295)( 73,320)( 74,319)( 75,301)( 76,302)( 77,299)( 78,300)( 79,314)( 80,313)( 81,306)( 82,305)( 83,292)( 84,291)( 85,293)( 86,294)( 87,311)( 88,312)( 89,304)( 90,303)( 91,318)( 92,317)( 93,316)( 94,315)( 95,298)( 96,297)( 97,257)( 98,258)( 99,276)(100,275)(101,277)(102,278)(103,264)(104,263)(105,288)(106,287)(107,269)(108,270)(109,267)(110,268)(111,282)(112,281)(113,274)(114,273)(115,260)(116,259)(117,261)(118,262)(119,279)(120,280)(121,272)(122,271)(123,286)(124,285)(125,284)(126,283)(127,266)(128,265)(129,225)(130,226)(131,244)(132,243)(133,245)(134,246)(135,232)(136,231)(137,256)(138,255)(139,237)(140,238)(141,235)(142,236)(143,250)(144,249)(145,242)(146,241)(147,228)(148,227)(149,229)(150,230)(151,247)(152,248)(153,240)(154,239)(155,254)(156,253)(157,252)(158,251)(159,234)(160,233)(321,353)(322,354)(323,372)(324,371)(325,373)(326,374)(327,360)(328,359)(329,384)(330,383)(331,365)(332,366)(333,363)(334,364)(335,378)(336,377)(337,370)(338,369)(339,356)(340,355)(341,357)(342,358)(343,375)(344,376)(345,368)(346,367)(347,382)(348,381)(349,380)(350,379)(351,362)(352,361)(385,449)(386,450)(387,468)(388,467)(389,469)(390,470)(391,456)(392,455)(393,480)(394,479)(395,461)(396,462)(397,459)(398,460)(399,474)(400,473)(401,466)(402,465)(403,452)(404,451)(405,453)(406,454)(407,471)(408,472)(409,464)(410,463)(411,478)(412,477)(413,476)(414,475)(415,458)(416,457)(419,436)(420,435)(421,437)(422,438)(423,424)(425,448)(426,447)(427,429)(428,430)(431,442)(432,441)(433,434)(443,446)(444,445);
s2 := Sym(480)!(  1,  3)(  2,  4)(  5,  6)(  7,  8)( 13, 16)( 14, 15)( 17, 30)( 18, 29)( 19, 32)( 20, 31)( 21, 28)( 22, 27)( 23, 26)( 24, 25)( 33,131)( 34,132)( 35,129)( 36,130)( 37,134)( 38,133)( 39,136)( 40,135)( 41,137)( 42,138)( 43,139)( 44,140)( 45,144)( 46,143)( 47,142)( 48,141)( 49,158)( 50,157)( 51,160)( 52,159)( 53,156)( 54,155)( 55,154)( 56,153)( 57,152)( 58,151)( 59,150)( 60,149)( 61,146)( 62,145)( 63,148)( 64,147)( 65, 99)( 66,100)( 67, 97)( 68, 98)( 69,102)( 70,101)( 71,104)( 72,103)( 73,105)( 74,106)( 75,107)( 76,108)( 77,112)( 78,111)( 79,110)( 80,109)( 81,126)( 82,125)( 83,128)( 84,127)( 85,124)( 86,123)( 87,122)( 88,121)( 89,120)( 90,119)( 91,118)( 92,117)( 93,114)( 94,113)( 95,116)( 96,115)(161,163)(162,164)(165,166)(167,168)(173,176)(174,175)(177,190)(178,189)(179,192)(180,191)(181,188)(182,187)(183,186)(184,185)(193,291)(194,292)(195,289)(196,290)(197,294)(198,293)(199,296)(200,295)(201,297)(202,298)(203,299)(204,300)(205,304)(206,303)(207,302)(208,301)(209,318)(210,317)(211,320)(212,319)(213,316)(214,315)(215,314)(216,313)(217,312)(218,311)(219,310)(220,309)(221,306)(222,305)(223,308)(224,307)(225,259)(226,260)(227,257)(228,258)(229,262)(230,261)(231,264)(232,263)(233,265)(234,266)(235,267)(236,268)(237,272)(238,271)(239,270)(240,269)(241,286)(242,285)(243,288)(244,287)(245,284)(246,283)(247,282)(248,281)(249,280)(250,279)(251,278)(252,277)(253,274)(254,273)(255,276)(256,275)(321,323)(322,324)(325,326)(327,328)(333,336)(334,335)(337,350)(338,349)(339,352)(340,351)(341,348)(342,347)(343,346)(344,345)(353,451)(354,452)(355,449)(356,450)(357,454)(358,453)(359,456)(360,455)(361,457)(362,458)(363,459)(364,460)(365,464)(366,463)(367,462)(368,461)(369,478)(370,477)(371,480)(372,479)(373,476)(374,475)(375,474)(376,473)(377,472)(378,471)(379,470)(380,469)(381,466)(382,465)(383,468)(384,467)(385,419)(386,420)(387,417)(388,418)(389,422)(390,421)(391,424)(392,423)(393,425)(394,426)(395,427)(396,428)(397,432)(398,431)(399,430)(400,429)(401,446)(402,445)(403,448)(404,447)(405,444)(406,443)(407,442)(408,441)(409,440)(410,439)(411,438)(412,437)(413,434)(414,433)(415,436)(416,435);
poly := sub<Sym(480)|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*s2*s1*s0*s1*s0*s1*s0*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, 
s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle