Polytope of Type {40,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,6}*1920a
if this polytope has a name.
Group : SmallGroup(1920,238293)
Rank : 3
Schlafli Type : {40,6}
Number of vertices, edges, etc : 160, 480, 24
Order of s0s1s2 : 30
Order of s0s1s2s1 : 8
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 : {40,6}*960c
   4-fold quotients : {20,6}*480c
   5-fold quotients : {8,6}*384d
   8-fold quotients : {20,6}*240b
   10-fold quotients : {8,6}*192a
   16-fold quotients : {10,6}*120
   20-fold quotients : {4,6}*96
   40-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {10,2}*40
   80-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {5,2}*20
   160-fold quotients : {2,3}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2> of order 2.
      16 facets:
         8 of {20}*40
         8 of {40}*80
      80 vertex figures:
         80 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0> of order 2.
      12 facets:
         12 of {40}*80
      80 vertex figures:
         80 of {6}*12
   P/N, where N=<s1*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 2.
      12 facets:
         12 of {40}*80
      80 vertex figures:
         80 of {6}*12
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      8 facets:
         4 of {20}*40
         4 of {40}*80
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 4.
      8 facets:
         4 of {20}*40
         4 of {40}*80
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1> of order 4.
      12 facets:
         8 of {10}*20
         4 of {40}*80
      40 vertex figures:
         40 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0> of order 4.
      8 facets:
         4 of {20}*40
         4 of {40}*80
      40 vertex figures:
         40 of {6}*12

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

Twisty Puzzle