Polytope of Type {30,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4}*960d
if this polytope has a name.
Group : SmallGroup(960,11375)
Rank : 3
Schlafli Type : {30,4}
Number of vertices, edges, etc : 120, 240, 16
Order of s0s1s2 : 15
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {30,4,2} of size 1920
Vertex Figure Of :
   {2,30,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {15,4}*480
   3-fold quotients : {10,4}*320b
   6-fold quotients : {5,4}*160
Covers (Minimal Covers in Boldface) :
   2-fold covers : {30,8}*1920j, {30,8}*1920k, {60,4}*1920h, {60,4}*1920i, {30,4}*1920d
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1> of order 2.
      8 facets:
         8 of {30}*60
      60 vertex figures:
         60 of {4}*8
   P/N, where N=<s1*s2*s1*s2> of order 2.
      8 facets:
         8 of {30}*60
      72 vertex figures:
         24 of {2}*4
         48 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 2.
      8 facets:
         8 of {30}*60
      60 vertex figures:
         60 of {4}*8
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 4.
      4 facets:
         4 of {30}*60
      36 vertex figures:
         12 of {2}*4
         24 of {4}*8
   P/N, where N=<s1*s2*s1*s2, s0*s1*s2*s1*s0*s2> of order 4.
      4 facets:
         4 of {30}*60
      42 vertex figures:
         24 of {2}*4
         18 of {4}*8
   P/N, where N=<s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      4 facets:
         4 of {30}*60
      36 vertex figures:
         12 of {2}*4
         24 of {4}*8

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

Twisty Puzzle