Polytope of Type {18,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,6}*1944h
if this polytope has a name.
Group : SmallGroup(1944,949)
Rank : 3
Schlafli Type : {18,6}
Number of vertices, edges, etc : 162, 486, 54
Order of s0s1s2 : 18
Order of s0s1s2s1 : 6
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 : {9,6}*972d
   3-fold quotients : {18,6}*648a, {18,6}*648d
   6-fold quotients : {9,6}*324a, {9,6}*324b
   9-fold quotients : {18,6}*216b, {6,6}*216c
   18-fold quotients : {9,6}*108, {3,6}*108
   27-fold quotients : {18,2}*72, {6,6}*72c
   54-fold quotients : {9,2}*36, {3,6}*36
   81-fold quotients : {6,2}*24
   162-fold quotients : {3,2}*12
   243-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*s1*s2*s1*s0*s1*s2*s1> of order 3.
      18 facets:
         18 of {18}*36
      54 vertex figures:
         54 of {6}*12
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1> of order 3.
      18 facets:
         18 of {18}*36
      54 vertex figures:
         54 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 3.
      18 facets:
         18 of {18}*36
      54 vertex figures:
         54 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1> of order 3.
      18 facets:
         18 of {18}*36
      90 vertex figures:
         36 of {6}*12
         54 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 3.
      18 facets:
         18 of {18}*36
      54 vertex figures:
         54 of {6}*12
   P/N, where N=<s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2> of order 3.
      36 facets:
         9 of {18}*36
         27 of {6}*12
      54 vertex figures:
         54 of {6}*12
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 3.
      18 facets:
         18 of {18}*36
      54 vertex figures:
         54 of {6}*12
   P/N, where N=<s1*s2*s1*s2, s0*s1*s2*s1*s0*s2> of order 9.
      6 facets:
         6 of {18}*36
      42 vertex figures:
         36 of {2}*4
         6 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 9.
      6 facets:
         6 of {18}*36
      30 vertex figures:
         12 of {6}*12
         18 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2, s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2> of order 9.
      12 facets:
         3 of {18}*36
         9 of {6}*12
      18 vertex figures:
         18 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2> of order 9.
      12 facets:
         3 of {18}*36
         9 of {6}*12
      30 vertex figures:
         12 of {6}*12
         18 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 9.
      6 facets:
         6 of {18}*36
      18 vertex figures:
         18 of {6}*12
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 9.
      6 facets:
         6 of {18}*36
      18 vertex figures:
         18 of {6}*12

Permutation Representation (GAP) : 
s0 := (  2,  3)(  5,  6)(  8,  9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)( 14, 24)( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 28, 55)( 29, 57)( 30, 56)( 31, 58)( 32, 60)( 33, 59)( 34, 61)( 35, 63)( 36, 62)( 37, 73)( 38, 75)( 39, 74)( 40, 76)( 41, 78)( 42, 77)( 43, 79)( 44, 81)( 45, 80)( 46, 64)( 47, 66)( 48, 65)( 49, 67)( 50, 69)( 51, 68)( 52, 70)( 53, 72)( 54, 71)( 82,172)( 83,174)( 84,173)( 85,175)( 86,177)( 87,176)( 88,178)( 89,180)( 90,179)( 91,163)( 92,165)( 93,164)( 94,166)( 95,168)( 96,167)( 97,169)( 98,171)( 99,170)(100,181)(101,183)(102,182)(103,184)(104,186)(105,185)(106,187)(107,189)(108,188)(109,226)(110,228)(111,227)(112,229)(113,231)(114,230)(115,232)(116,234)(117,233)(118,217)(119,219)(120,218)(121,220)(122,222)(123,221)(124,223)(125,225)(126,224)(127,235)(128,237)(129,236)(130,238)(131,240)(132,239)(133,241)(134,243)(135,242)(136,199)(137,201)(138,200)(139,202)(140,204)(141,203)(142,205)(143,207)(144,206)(145,190)(146,192)(147,191)(148,193)(149,195)(150,194)(151,196)(152,198)(153,197)(154,208)(155,210)(156,209)(157,211)(158,213)(159,212)(160,214)(161,216)(162,215)(245,246)(248,249)(251,252)(253,262)(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)(260,270)(261,269)(271,298)(272,300)(273,299)(274,301)(275,303)(276,302)(277,304)(278,306)(279,305)(280,316)(281,318)(282,317)(283,319)(284,321)(285,320)(286,322)(287,324)(288,323)(289,307)(290,309)(291,308)(292,310)(293,312)(294,311)(295,313)(296,315)(297,314)(325,415)(326,417)(327,416)(328,418)(329,420)(330,419)(331,421)(332,423)(333,422)(334,406)(335,408)(336,407)(337,409)(338,411)(339,410)(340,412)(341,414)(342,413)(343,424)(344,426)(345,425)(346,427)(347,429)(348,428)(349,430)(350,432)(351,431)(352,469)(353,471)(354,470)(355,472)(356,474)(357,473)(358,475)(359,477)(360,476)(361,460)(362,462)(363,461)(364,463)(365,465)(366,464)(367,466)(368,468)(369,467)(370,478)(371,480)(372,479)(373,481)(374,483)(375,482)(376,484)(377,486)(378,485)(379,442)(380,444)(381,443)(382,445)(383,447)(384,446)(385,448)(386,450)(387,449)(388,433)(389,435)(390,434)(391,436)(392,438)(393,437)(394,439)(395,441)(396,440)(397,451)(398,453)(399,452)(400,454)(401,456)(402,455)(403,457)(404,459)(405,458);;
s1 := (  1,436)(  2,438)(  3,437)(  4,440)(  5,439)(  6,441)(  7,435)(  8,434)(  9,433)( 10,454)( 11,456)( 12,455)( 13,458)( 14,457)( 15,459)( 16,453)( 17,452)( 18,451)( 19,445)( 20,447)( 21,446)( 22,449)( 23,448)( 24,450)( 25,444)( 26,443)( 27,442)( 28,414)( 29,413)( 30,412)( 31,406)( 32,408)( 33,407)( 34,410)( 35,409)( 36,411)( 37,432)( 38,431)( 39,430)( 40,424)( 41,426)( 42,425)( 43,428)( 44,427)( 45,429)( 46,423)( 47,422)( 48,421)( 49,415)( 50,417)( 51,416)( 52,419)( 53,418)( 54,420)( 55,461)( 56,460)( 57,462)( 58,465)( 59,464)( 60,463)( 61,466)( 62,468)( 63,467)( 64,479)( 65,478)( 66,480)( 67,483)( 68,482)( 69,481)( 70,484)( 71,486)( 72,485)( 73,470)( 74,469)( 75,471)( 76,474)( 77,473)( 78,472)( 79,475)( 80,477)( 81,476)( 82,355)( 83,357)( 84,356)( 85,359)( 86,358)( 87,360)( 88,354)( 89,353)( 90,352)( 91,373)( 92,375)( 93,374)( 94,377)( 95,376)( 96,378)( 97,372)( 98,371)( 99,370)(100,364)(101,366)(102,365)(103,368)(104,367)(105,369)(106,363)(107,362)(108,361)(109,333)(110,332)(111,331)(112,325)(113,327)(114,326)(115,329)(116,328)(117,330)(118,351)(119,350)(120,349)(121,343)(122,345)(123,344)(124,347)(125,346)(126,348)(127,342)(128,341)(129,340)(130,334)(131,336)(132,335)(133,338)(134,337)(135,339)(136,380)(137,379)(138,381)(139,384)(140,383)(141,382)(142,385)(143,387)(144,386)(145,398)(146,397)(147,399)(148,402)(149,401)(150,400)(151,403)(152,405)(153,404)(154,389)(155,388)(156,390)(157,393)(158,392)(159,391)(160,394)(161,396)(162,395)(163,274)(164,276)(165,275)(166,278)(167,277)(168,279)(169,273)(170,272)(171,271)(172,292)(173,294)(174,293)(175,296)(176,295)(177,297)(178,291)(179,290)(180,289)(181,283)(182,285)(183,284)(184,287)(185,286)(186,288)(187,282)(188,281)(189,280)(190,252)(191,251)(192,250)(193,244)(194,246)(195,245)(196,248)(197,247)(198,249)(199,270)(200,269)(201,268)(202,262)(203,264)(204,263)(205,266)(206,265)(207,267)(208,261)(209,260)(210,259)(211,253)(212,255)(213,254)(214,257)(215,256)(216,258)(217,299)(218,298)(219,300)(220,303)(221,302)(222,301)(223,304)(224,306)(225,305)(226,317)(227,316)(228,318)(229,321)(230,320)(231,319)(232,322)(233,324)(234,323)(235,308)(236,307)(237,309)(238,312)(239,311)(240,310)(241,313)(242,315)(243,314);;
s2 := (  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 55)( 29, 57)( 30, 56)( 31, 61)( 32, 63)( 33, 62)( 34, 58)( 35, 60)( 36, 59)( 37, 64)( 38, 66)( 39, 65)( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)( 45, 68)( 46, 73)( 47, 75)( 48, 74)( 49, 79)( 50, 81)( 51, 80)( 52, 76)( 53, 78)( 54, 77)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(109,136)(110,138)(111,137)(112,142)(113,144)(114,143)(115,139)(116,141)(117,140)(118,145)(119,147)(120,146)(121,151)(122,153)(123,152)(124,148)(125,150)(126,149)(127,154)(128,156)(129,155)(130,160)(131,162)(132,161)(133,157)(134,159)(135,158)(164,165)(166,169)(167,171)(168,170)(173,174)(175,178)(176,180)(177,179)(182,183)(184,187)(185,189)(186,188)(190,217)(191,219)(192,218)(193,223)(194,225)(195,224)(196,220)(197,222)(198,221)(199,226)(200,228)(201,227)(202,232)(203,234)(204,233)(205,229)(206,231)(207,230)(208,235)(209,237)(210,236)(211,241)(212,243)(213,242)(214,238)(215,240)(216,239)(245,246)(247,250)(248,252)(249,251)(254,255)(256,259)(257,261)(258,260)(263,264)(265,268)(266,270)(267,269)(271,298)(272,300)(273,299)(274,304)(275,306)(276,305)(277,301)(278,303)(279,302)(280,307)(281,309)(282,308)(283,313)(284,315)(285,314)(286,310)(287,312)(288,311)(289,316)(290,318)(291,317)(292,322)(293,324)(294,323)(295,319)(296,321)(297,320)(326,327)(328,331)(329,333)(330,332)(335,336)(337,340)(338,342)(339,341)(344,345)(346,349)(347,351)(348,350)(352,379)(353,381)(354,380)(355,385)(356,387)(357,386)(358,382)(359,384)(360,383)(361,388)(362,390)(363,389)(364,394)(365,396)(366,395)(367,391)(368,393)(369,392)(370,397)(371,399)(372,398)(373,403)(374,405)(375,404)(376,400)(377,402)(378,401)(407,408)(409,412)(410,414)(411,413)(416,417)(418,421)(419,423)(420,422)(425,426)(427,430)(428,432)(429,431)(433,460)(434,462)(435,461)(436,466)(437,468)(438,467)(439,463)(440,465)(441,464)(442,469)(443,471)(444,470)(445,475)(446,477)(447,476)(448,472)(449,474)(450,473)(451,478)(452,480)(453,479)(454,484)(455,486)(456,485)(457,481)(458,483)(459,482);;
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, 
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(486)!(  2,  3)(  5,  6)(  8,  9)( 10, 19)( 11, 21)( 12, 20)( 13, 22)( 14, 24)( 15, 23)( 16, 25)( 17, 27)( 18, 26)( 28, 55)( 29, 57)( 30, 56)( 31, 58)( 32, 60)( 33, 59)( 34, 61)( 35, 63)( 36, 62)( 37, 73)( 38, 75)( 39, 74)( 40, 76)( 41, 78)( 42, 77)( 43, 79)( 44, 81)( 45, 80)( 46, 64)( 47, 66)( 48, 65)( 49, 67)( 50, 69)( 51, 68)( 52, 70)( 53, 72)( 54, 71)( 82,172)( 83,174)( 84,173)( 85,175)( 86,177)( 87,176)( 88,178)( 89,180)( 90,179)( 91,163)( 92,165)( 93,164)( 94,166)( 95,168)( 96,167)( 97,169)( 98,171)( 99,170)(100,181)(101,183)(102,182)(103,184)(104,186)(105,185)(106,187)(107,189)(108,188)(109,226)(110,228)(111,227)(112,229)(113,231)(114,230)(115,232)(116,234)(117,233)(118,217)(119,219)(120,218)(121,220)(122,222)(123,221)(124,223)(125,225)(126,224)(127,235)(128,237)(129,236)(130,238)(131,240)(132,239)(133,241)(134,243)(135,242)(136,199)(137,201)(138,200)(139,202)(140,204)(141,203)(142,205)(143,207)(144,206)(145,190)(146,192)(147,191)(148,193)(149,195)(150,194)(151,196)(152,198)(153,197)(154,208)(155,210)(156,209)(157,211)(158,213)(159,212)(160,214)(161,216)(162,215)(245,246)(248,249)(251,252)(253,262)(254,264)(255,263)(256,265)(257,267)(258,266)(259,268)(260,270)(261,269)(271,298)(272,300)(273,299)(274,301)(275,303)(276,302)(277,304)(278,306)(279,305)(280,316)(281,318)(282,317)(283,319)(284,321)(285,320)(286,322)(287,324)(288,323)(289,307)(290,309)(291,308)(292,310)(293,312)(294,311)(295,313)(296,315)(297,314)(325,415)(326,417)(327,416)(328,418)(329,420)(330,419)(331,421)(332,423)(333,422)(334,406)(335,408)(336,407)(337,409)(338,411)(339,410)(340,412)(341,414)(342,413)(343,424)(344,426)(345,425)(346,427)(347,429)(348,428)(349,430)(350,432)(351,431)(352,469)(353,471)(354,470)(355,472)(356,474)(357,473)(358,475)(359,477)(360,476)(361,460)(362,462)(363,461)(364,463)(365,465)(366,464)(367,466)(368,468)(369,467)(370,478)(371,480)(372,479)(373,481)(374,483)(375,482)(376,484)(377,486)(378,485)(379,442)(380,444)(381,443)(382,445)(383,447)(384,446)(385,448)(386,450)(387,449)(388,433)(389,435)(390,434)(391,436)(392,438)(393,437)(394,439)(395,441)(396,440)(397,451)(398,453)(399,452)(400,454)(401,456)(402,455)(403,457)(404,459)(405,458);
s1 := Sym(486)!(  1,436)(  2,438)(  3,437)(  4,440)(  5,439)(  6,441)(  7,435)(  8,434)(  9,433)( 10,454)( 11,456)( 12,455)( 13,458)( 14,457)( 15,459)( 16,453)( 17,452)( 18,451)( 19,445)( 20,447)( 21,446)( 22,449)( 23,448)( 24,450)( 25,444)( 26,443)( 27,442)( 28,414)( 29,413)( 30,412)( 31,406)( 32,408)( 33,407)( 34,410)( 35,409)( 36,411)( 37,432)( 38,431)( 39,430)( 40,424)( 41,426)( 42,425)( 43,428)( 44,427)( 45,429)( 46,423)( 47,422)( 48,421)( 49,415)( 50,417)( 51,416)( 52,419)( 53,418)( 54,420)( 55,461)( 56,460)( 57,462)( 58,465)( 59,464)( 60,463)( 61,466)( 62,468)( 63,467)( 64,479)( 65,478)( 66,480)( 67,483)( 68,482)( 69,481)( 70,484)( 71,486)( 72,485)( 73,470)( 74,469)( 75,471)( 76,474)( 77,473)( 78,472)( 79,475)( 80,477)( 81,476)( 82,355)( 83,357)( 84,356)( 85,359)( 86,358)( 87,360)( 88,354)( 89,353)( 90,352)( 91,373)( 92,375)( 93,374)( 94,377)( 95,376)( 96,378)( 97,372)( 98,371)( 99,370)(100,364)(101,366)(102,365)(103,368)(104,367)(105,369)(106,363)(107,362)(108,361)(109,333)(110,332)(111,331)(112,325)(113,327)(114,326)(115,329)(116,328)(117,330)(118,351)(119,350)(120,349)(121,343)(122,345)(123,344)(124,347)(125,346)(126,348)(127,342)(128,341)(129,340)(130,334)(131,336)(132,335)(133,338)(134,337)(135,339)(136,380)(137,379)(138,381)(139,384)(140,383)(141,382)(142,385)(143,387)(144,386)(145,398)(146,397)(147,399)(148,402)(149,401)(150,400)(151,403)(152,405)(153,404)(154,389)(155,388)(156,390)(157,393)(158,392)(159,391)(160,394)(161,396)(162,395)(163,274)(164,276)(165,275)(166,278)(167,277)(168,279)(169,273)(170,272)(171,271)(172,292)(173,294)(174,293)(175,296)(176,295)(177,297)(178,291)(179,290)(180,289)(181,283)(182,285)(183,284)(184,287)(185,286)(186,288)(187,282)(188,281)(189,280)(190,252)(191,251)(192,250)(193,244)(194,246)(195,245)(196,248)(197,247)(198,249)(199,270)(200,269)(201,268)(202,262)(203,264)(204,263)(205,266)(206,265)(207,267)(208,261)(209,260)(210,259)(211,253)(212,255)(213,254)(214,257)(215,256)(216,258)(217,299)(218,298)(219,300)(220,303)(221,302)(222,301)(223,304)(224,306)(225,305)(226,317)(227,316)(228,318)(229,321)(230,320)(231,319)(232,322)(233,324)(234,323)(235,308)(236,307)(237,309)(238,312)(239,311)(240,310)(241,313)(242,315)(243,314);
s2 := Sym(486)!(  2,  3)(  4,  7)(  5,  9)(  6,  8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 28, 55)( 29, 57)( 30, 56)( 31, 61)( 32, 63)( 33, 62)( 34, 58)( 35, 60)( 36, 59)( 37, 64)( 38, 66)( 39, 65)( 40, 70)( 41, 72)( 42, 71)( 43, 67)( 44, 69)( 45, 68)( 46, 73)( 47, 75)( 48, 74)( 49, 79)( 50, 81)( 51, 80)( 52, 76)( 53, 78)( 54, 77)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 92, 93)( 94, 97)( 95, 99)( 96, 98)(101,102)(103,106)(104,108)(105,107)(109,136)(110,138)(111,137)(112,142)(113,144)(114,143)(115,139)(116,141)(117,140)(118,145)(119,147)(120,146)(121,151)(122,153)(123,152)(124,148)(125,150)(126,149)(127,154)(128,156)(129,155)(130,160)(131,162)(132,161)(133,157)(134,159)(135,158)(164,165)(166,169)(167,171)(168,170)(173,174)(175,178)(176,180)(177,179)(182,183)(184,187)(185,189)(186,188)(190,217)(191,219)(192,218)(193,223)(194,225)(195,224)(196,220)(197,222)(198,221)(199,226)(200,228)(201,227)(202,232)(203,234)(204,233)(205,229)(206,231)(207,230)(208,235)(209,237)(210,236)(211,241)(212,243)(213,242)(214,238)(215,240)(216,239)(245,246)(247,250)(248,252)(249,251)(254,255)(256,259)(257,261)(258,260)(263,264)(265,268)(266,270)(267,269)(271,298)(272,300)(273,299)(274,304)(275,306)(276,305)(277,301)(278,303)(279,302)(280,307)(281,309)(282,308)(283,313)(284,315)(285,314)(286,310)(287,312)(288,311)(289,316)(290,318)(291,317)(292,322)(293,324)(294,323)(295,319)(296,321)(297,320)(326,327)(328,331)(329,333)(330,332)(335,336)(337,340)(338,342)(339,341)(344,345)(346,349)(347,351)(348,350)(352,379)(353,381)(354,380)(355,385)(356,387)(357,386)(358,382)(359,384)(360,383)(361,388)(362,390)(363,389)(364,394)(365,396)(366,395)(367,391)(368,393)(369,392)(370,397)(371,399)(372,398)(373,403)(374,405)(375,404)(376,400)(377,402)(378,401)(407,408)(409,412)(410,414)(411,413)(416,417)(418,421)(419,423)(420,422)(425,426)(427,430)(428,432)(429,431)(433,460)(434,462)(435,461)(436,466)(437,468)(438,467)(439,463)(440,465)(441,464)(442,469)(443,471)(444,470)(445,475)(446,477)(447,476)(448,472)(449,474)(450,473)(451,478)(452,480)(453,479)(454,484)(455,486)(456,485)(457,481)(458,483)(459,482);
poly := sub<Sym(486)|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, 
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope

Twisty Puzzle