Polytope of Type {8,36}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,36}*1152c
if this polytope has a name.
Group : SmallGroup(1152,153963)
Rank : 3
Schlafli Type : {8,36}
Number of vertices, edges, etc : 16, 288, 72
Order of s0s1s2 : 9
Order of s0s1s2s1 : 8
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) :
   2-fold quotients : {8,18}*576a
   3-fold quotients : {8,12}*384c
   6-fold quotients : {8,6}*192a
   8-fold quotients : {4,18}*144c
   16-fold quotients : {4,9}*72
   24-fold quotients : {4,6}*48b
   48-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1> of order 2.
      48 facets:
         24 of {8}*16
         24 of {4}*8
      8 vertex figures:
         8 of {36}*72

Permutation Representation (GAP) : 
s0 := (  1,305)(  2,306)(  3,307)(  4,308)(  5,309)(  6,310)(  7,311)(  8,312)(  9,320)( 10,319)( 11,318)( 12,317)( 13,316)( 14,315)( 15,314)( 16,313)( 17,295)( 18,296)( 19,293)( 20,294)( 21,291)( 22,292)( 23,289)( 24,290)( 25,298)( 26,297)( 27,300)( 28,299)( 29,302)( 30,301)( 31,304)( 32,303)( 33,337)( 34,338)( 35,339)( 36,340)( 37,341)( 38,342)( 39,343)( 40,344)( 41,352)( 42,351)( 43,350)( 44,349)( 45,348)( 46,347)( 47,346)( 48,345)( 49,327)( 50,328)( 51,325)( 52,326)( 53,323)( 54,324)( 55,321)( 56,322)( 57,330)( 58,329)( 59,332)( 60,331)( 61,334)( 62,333)( 63,336)( 64,335)( 65,369)( 66,370)( 67,371)( 68,372)( 69,373)( 70,374)( 71,375)( 72,376)( 73,384)( 74,383)( 75,382)( 76,381)( 77,380)( 78,379)( 79,378)( 80,377)( 81,359)( 82,360)( 83,357)( 84,358)( 85,355)( 86,356)( 87,353)( 88,354)( 89,362)( 90,361)( 91,364)( 92,363)( 93,366)( 94,365)( 95,368)( 96,367)( 97,401)( 98,402)( 99,403)(100,404)(101,405)(102,406)(103,407)(104,408)(105,416)(106,415)(107,414)(108,413)(109,412)(110,411)(111,410)(112,409)(113,391)(114,392)(115,389)(116,390)(117,387)(118,388)(119,385)(120,386)(121,394)(122,393)(123,396)(124,395)(125,398)(126,397)(127,400)(128,399)(129,433)(130,434)(131,435)(132,436)(133,437)(134,438)(135,439)(136,440)(137,448)(138,447)(139,446)(140,445)(141,444)(142,443)(143,442)(144,441)(145,423)(146,424)(147,421)(148,422)(149,419)(150,420)(151,417)(152,418)(153,426)(154,425)(155,428)(156,427)(157,430)(158,429)(159,432)(160,431)(161,465)(162,466)(163,467)(164,468)(165,469)(166,470)(167,471)(168,472)(169,480)(170,479)(171,478)(172,477)(173,476)(174,475)(175,474)(176,473)(177,455)(178,456)(179,453)(180,454)(181,451)(182,452)(183,449)(184,450)(185,458)(186,457)(187,460)(188,459)(189,462)(190,461)(191,464)(192,463)(193,497)(194,498)(195,499)(196,500)(197,501)(198,502)(199,503)(200,504)(201,512)(202,511)(203,510)(204,509)(205,508)(206,507)(207,506)(208,505)(209,487)(210,488)(211,485)(212,486)(213,483)(214,484)(215,481)(216,482)(217,490)(218,489)(219,492)(220,491)(221,494)(222,493)(223,496)(224,495)(225,529)(226,530)(227,531)(228,532)(229,533)(230,534)(231,535)(232,536)(233,544)(234,543)(235,542)(236,541)(237,540)(238,539)(239,538)(240,537)(241,519)(242,520)(243,517)(244,518)(245,515)(246,516)(247,513)(248,514)(249,522)(250,521)(251,524)(252,523)(253,526)(254,525)(255,528)(256,527)(257,561)(258,562)(259,563)(260,564)(261,565)(262,566)(263,567)(264,568)(265,576)(266,575)(267,574)(268,573)(269,572)(270,571)(271,570)(272,569)(273,551)(274,552)(275,549)(276,550)(277,547)(278,548)(279,545)(280,546)(281,554)(282,553)(283,556)(284,555)(285,558)(286,557)(287,560)(288,559);;
s1 := (  3,  4)(  5,  6)(  9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 26)( 18, 25)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 70)( 38, 69)( 39, 71)( 40, 72)( 41, 80)( 42, 79)( 43, 77)( 44, 78)( 45, 75)( 46, 76)( 47, 74)( 48, 73)( 49, 90)( 50, 89)( 51, 91)( 52, 92)( 53, 93)( 54, 94)( 55, 96)( 56, 95)( 57, 82)( 58, 81)( 59, 83)( 60, 84)( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 97,257)( 98,258)( 99,260)(100,259)(101,262)(102,261)(103,263)(104,264)(105,272)(106,271)(107,269)(108,270)(109,267)(110,268)(111,266)(112,265)(113,282)(114,281)(115,283)(116,284)(117,285)(118,286)(119,288)(120,287)(121,274)(122,273)(123,275)(124,276)(125,277)(126,278)(127,280)(128,279)(129,225)(130,226)(131,228)(132,227)(133,230)(134,229)(135,231)(136,232)(137,240)(138,239)(139,237)(140,238)(141,235)(142,236)(143,234)(144,233)(145,250)(146,249)(147,251)(148,252)(149,253)(150,254)(151,256)(152,255)(153,242)(154,241)(155,243)(156,244)(157,245)(158,246)(159,248)(160,247)(161,193)(162,194)(163,196)(164,195)(165,198)(166,197)(167,199)(168,200)(169,208)(170,207)(171,205)(172,206)(173,203)(174,204)(175,202)(176,201)(177,218)(178,217)(179,219)(180,220)(181,221)(182,222)(183,224)(184,223)(185,210)(186,209)(187,211)(188,212)(189,213)(190,214)(191,216)(192,215)(289,295)(290,296)(291,294)(292,293)(297,298)(303,304)(305,320)(306,319)(307,317)(308,318)(309,315)(310,316)(311,314)(312,313)(321,359)(322,360)(323,358)(324,357)(325,356)(326,355)(327,353)(328,354)(329,362)(330,361)(331,363)(332,364)(333,365)(334,366)(335,368)(336,367)(337,384)(338,383)(339,381)(340,382)(341,379)(342,380)(343,378)(344,377)(345,376)(346,375)(347,373)(348,374)(349,371)(350,372)(351,370)(352,369)(385,551)(386,552)(387,550)(388,549)(389,548)(390,547)(391,545)(392,546)(393,554)(394,553)(395,555)(396,556)(397,557)(398,558)(399,560)(400,559)(401,576)(402,575)(403,573)(404,574)(405,571)(406,572)(407,570)(408,569)(409,568)(410,567)(411,565)(412,566)(413,563)(414,564)(415,562)(416,561)(417,519)(418,520)(419,518)(420,517)(421,516)(422,515)(423,513)(424,514)(425,522)(426,521)(427,523)(428,524)(429,525)(430,526)(431,528)(432,527)(433,544)(434,543)(435,541)(436,542)(437,539)(438,540)(439,538)(440,537)(441,536)(442,535)(443,533)(444,534)(445,531)(446,532)(447,530)(448,529)(449,487)(450,488)(451,486)(452,485)(453,484)(454,483)(455,481)(456,482)(457,490)(458,489)(459,491)(460,492)(461,493)(462,494)(463,496)(464,495)(465,512)(466,511)(467,509)(468,510)(469,507)(470,508)(471,506)(472,505)(473,504)(474,503)(475,501)(476,502)(477,499)(478,500)(479,498)(480,497);;
s2 := (  1,401)(  2,404)(  3,403)(  4,402)(  5,405)(  6,408)(  7,407)(  8,406)(  9,395)( 10,394)( 11,393)( 12,396)( 13,399)( 14,398)( 15,397)( 16,400)( 17,385)( 18,388)( 19,387)( 20,386)( 21,389)( 22,392)( 23,391)( 24,390)( 25,415)( 26,414)( 27,413)( 28,416)( 29,411)( 30,410)( 31,409)( 32,412)( 33,465)( 34,468)( 35,467)( 36,466)( 37,469)( 38,472)( 39,471)( 40,470)( 41,459)( 42,458)( 43,457)( 44,460)( 45,463)( 46,462)( 47,461)( 48,464)( 49,449)( 50,452)( 51,451)( 52,450)( 53,453)( 54,456)( 55,455)( 56,454)( 57,479)( 58,478)( 59,477)( 60,480)( 61,475)( 62,474)( 63,473)( 64,476)( 65,433)( 66,436)( 67,435)( 68,434)( 69,437)( 70,440)( 71,439)( 72,438)( 73,427)( 74,426)( 75,425)( 76,428)( 77,431)( 78,430)( 79,429)( 80,432)( 81,417)( 82,420)( 83,419)( 84,418)( 85,421)( 86,424)( 87,423)( 88,422)( 89,447)( 90,446)( 91,445)( 92,448)( 93,443)( 94,442)( 95,441)( 96,444)( 97,305)( 98,308)( 99,307)(100,306)(101,309)(102,312)(103,311)(104,310)(105,299)(106,298)(107,297)(108,300)(109,303)(110,302)(111,301)(112,304)(113,289)(114,292)(115,291)(116,290)(117,293)(118,296)(119,295)(120,294)(121,319)(122,318)(123,317)(124,320)(125,315)(126,314)(127,313)(128,316)(129,369)(130,372)(131,371)(132,370)(133,373)(134,376)(135,375)(136,374)(137,363)(138,362)(139,361)(140,364)(141,367)(142,366)(143,365)(144,368)(145,353)(146,356)(147,355)(148,354)(149,357)(150,360)(151,359)(152,358)(153,383)(154,382)(155,381)(156,384)(157,379)(158,378)(159,377)(160,380)(161,337)(162,340)(163,339)(164,338)(165,341)(166,344)(167,343)(168,342)(169,331)(170,330)(171,329)(172,332)(173,335)(174,334)(175,333)(176,336)(177,321)(178,324)(179,323)(180,322)(181,325)(182,328)(183,327)(184,326)(185,351)(186,350)(187,349)(188,352)(189,347)(190,346)(191,345)(192,348)(193,561)(194,564)(195,563)(196,562)(197,565)(198,568)(199,567)(200,566)(201,555)(202,554)(203,553)(204,556)(205,559)(206,558)(207,557)(208,560)(209,545)(210,548)(211,547)(212,546)(213,549)(214,552)(215,551)(216,550)(217,575)(218,574)(219,573)(220,576)(221,571)(222,570)(223,569)(224,572)(225,529)(226,532)(227,531)(228,530)(229,533)(230,536)(231,535)(232,534)(233,523)(234,522)(235,521)(236,524)(237,527)(238,526)(239,525)(240,528)(241,513)(242,516)(243,515)(244,514)(245,517)(246,520)(247,519)(248,518)(249,543)(250,542)(251,541)(252,544)(253,539)(254,538)(255,537)(256,540)(257,497)(258,500)(259,499)(260,498)(261,501)(262,504)(263,503)(264,502)(265,491)(266,490)(267,489)(268,492)(269,495)(270,494)(271,493)(272,496)(273,481)(274,484)(275,483)(276,482)(277,485)(278,488)(279,487)(280,486)(281,511)(282,510)(283,509)(284,512)(285,507)(286,506)(287,505)(288,508);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(576)!(  1,305)(  2,306)(  3,307)(  4,308)(  5,309)(  6,310)(  7,311)(  8,312)(  9,320)( 10,319)( 11,318)( 12,317)( 13,316)( 14,315)( 15,314)( 16,313)( 17,295)( 18,296)( 19,293)( 20,294)( 21,291)( 22,292)( 23,289)( 24,290)( 25,298)( 26,297)( 27,300)( 28,299)( 29,302)( 30,301)( 31,304)( 32,303)( 33,337)( 34,338)( 35,339)( 36,340)( 37,341)( 38,342)( 39,343)( 40,344)( 41,352)( 42,351)( 43,350)( 44,349)( 45,348)( 46,347)( 47,346)( 48,345)( 49,327)( 50,328)( 51,325)( 52,326)( 53,323)( 54,324)( 55,321)( 56,322)( 57,330)( 58,329)( 59,332)( 60,331)( 61,334)( 62,333)( 63,336)( 64,335)( 65,369)( 66,370)( 67,371)( 68,372)( 69,373)( 70,374)( 71,375)( 72,376)( 73,384)( 74,383)( 75,382)( 76,381)( 77,380)( 78,379)( 79,378)( 80,377)( 81,359)( 82,360)( 83,357)( 84,358)( 85,355)( 86,356)( 87,353)( 88,354)( 89,362)( 90,361)( 91,364)( 92,363)( 93,366)( 94,365)( 95,368)( 96,367)( 97,401)( 98,402)( 99,403)(100,404)(101,405)(102,406)(103,407)(104,408)(105,416)(106,415)(107,414)(108,413)(109,412)(110,411)(111,410)(112,409)(113,391)(114,392)(115,389)(116,390)(117,387)(118,388)(119,385)(120,386)(121,394)(122,393)(123,396)(124,395)(125,398)(126,397)(127,400)(128,399)(129,433)(130,434)(131,435)(132,436)(133,437)(134,438)(135,439)(136,440)(137,448)(138,447)(139,446)(140,445)(141,444)(142,443)(143,442)(144,441)(145,423)(146,424)(147,421)(148,422)(149,419)(150,420)(151,417)(152,418)(153,426)(154,425)(155,428)(156,427)(157,430)(158,429)(159,432)(160,431)(161,465)(162,466)(163,467)(164,468)(165,469)(166,470)(167,471)(168,472)(169,480)(170,479)(171,478)(172,477)(173,476)(174,475)(175,474)(176,473)(177,455)(178,456)(179,453)(180,454)(181,451)(182,452)(183,449)(184,450)(185,458)(186,457)(187,460)(188,459)(189,462)(190,461)(191,464)(192,463)(193,497)(194,498)(195,499)(196,500)(197,501)(198,502)(199,503)(200,504)(201,512)(202,511)(203,510)(204,509)(205,508)(206,507)(207,506)(208,505)(209,487)(210,488)(211,485)(212,486)(213,483)(214,484)(215,481)(216,482)(217,490)(218,489)(219,492)(220,491)(221,494)(222,493)(223,496)(224,495)(225,529)(226,530)(227,531)(228,532)(229,533)(230,534)(231,535)(232,536)(233,544)(234,543)(235,542)(236,541)(237,540)(238,539)(239,538)(240,537)(241,519)(242,520)(243,517)(244,518)(245,515)(246,516)(247,513)(248,514)(249,522)(250,521)(251,524)(252,523)(253,526)(254,525)(255,528)(256,527)(257,561)(258,562)(259,563)(260,564)(261,565)(262,566)(263,567)(264,568)(265,576)(266,575)(267,574)(268,573)(269,572)(270,571)(271,570)(272,569)(273,551)(274,552)(275,549)(276,550)(277,547)(278,548)(279,545)(280,546)(281,554)(282,553)(283,556)(284,555)(285,558)(286,557)(287,560)(288,559);
s1 := Sym(576)!(  3,  4)(  5,  6)(  9, 16)( 10, 15)( 11, 13)( 12, 14)( 17, 26)( 18, 25)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 70)( 38, 69)( 39, 71)( 40, 72)( 41, 80)( 42, 79)( 43, 77)( 44, 78)( 45, 75)( 46, 76)( 47, 74)( 48, 73)( 49, 90)( 50, 89)( 51, 91)( 52, 92)( 53, 93)( 54, 94)( 55, 96)( 56, 95)( 57, 82)( 58, 81)( 59, 83)( 60, 84)( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 97,257)( 98,258)( 99,260)(100,259)(101,262)(102,261)(103,263)(104,264)(105,272)(106,271)(107,269)(108,270)(109,267)(110,268)(111,266)(112,265)(113,282)(114,281)(115,283)(116,284)(117,285)(118,286)(119,288)(120,287)(121,274)(122,273)(123,275)(124,276)(125,277)(126,278)(127,280)(128,279)(129,225)(130,226)(131,228)(132,227)(133,230)(134,229)(135,231)(136,232)(137,240)(138,239)(139,237)(140,238)(141,235)(142,236)(143,234)(144,233)(145,250)(146,249)(147,251)(148,252)(149,253)(150,254)(151,256)(152,255)(153,242)(154,241)(155,243)(156,244)(157,245)(158,246)(159,248)(160,247)(161,193)(162,194)(163,196)(164,195)(165,198)(166,197)(167,199)(168,200)(169,208)(170,207)(171,205)(172,206)(173,203)(174,204)(175,202)(176,201)(177,218)(178,217)(179,219)(180,220)(181,221)(182,222)(183,224)(184,223)(185,210)(186,209)(187,211)(188,212)(189,213)(190,214)(191,216)(192,215)(289,295)(290,296)(291,294)(292,293)(297,298)(303,304)(305,320)(306,319)(307,317)(308,318)(309,315)(310,316)(311,314)(312,313)(321,359)(322,360)(323,358)(324,357)(325,356)(326,355)(327,353)(328,354)(329,362)(330,361)(331,363)(332,364)(333,365)(334,366)(335,368)(336,367)(337,384)(338,383)(339,381)(340,382)(341,379)(342,380)(343,378)(344,377)(345,376)(346,375)(347,373)(348,374)(349,371)(350,372)(351,370)(352,369)(385,551)(386,552)(387,550)(388,549)(389,548)(390,547)(391,545)(392,546)(393,554)(394,553)(395,555)(396,556)(397,557)(398,558)(399,560)(400,559)(401,576)(402,575)(403,573)(404,574)(405,571)(406,572)(407,570)(408,569)(409,568)(410,567)(411,565)(412,566)(413,563)(414,564)(415,562)(416,561)(417,519)(418,520)(419,518)(420,517)(421,516)(422,515)(423,513)(424,514)(425,522)(426,521)(427,523)(428,524)(429,525)(430,526)(431,528)(432,527)(433,544)(434,543)(435,541)(436,542)(437,539)(438,540)(439,538)(440,537)(441,536)(442,535)(443,533)(444,534)(445,531)(446,532)(447,530)(448,529)(449,487)(450,488)(451,486)(452,485)(453,484)(454,483)(455,481)(456,482)(457,490)(458,489)(459,491)(460,492)(461,493)(462,494)(463,496)(464,495)(465,512)(466,511)(467,509)(468,510)(469,507)(470,508)(471,506)(472,505)(473,504)(474,503)(475,501)(476,502)(477,499)(478,500)(479,498)(480,497);
s2 := Sym(576)!(  1,401)(  2,404)(  3,403)(  4,402)(  5,405)(  6,408)(  7,407)(  8,406)(  9,395)( 10,394)( 11,393)( 12,396)( 13,399)( 14,398)( 15,397)( 16,400)( 17,385)( 18,388)( 19,387)( 20,386)( 21,389)( 22,392)( 23,391)( 24,390)( 25,415)( 26,414)( 27,413)( 28,416)( 29,411)( 30,410)( 31,409)( 32,412)( 33,465)( 34,468)( 35,467)( 36,466)( 37,469)( 38,472)( 39,471)( 40,470)( 41,459)( 42,458)( 43,457)( 44,460)( 45,463)( 46,462)( 47,461)( 48,464)( 49,449)( 50,452)( 51,451)( 52,450)( 53,453)( 54,456)( 55,455)( 56,454)( 57,479)( 58,478)( 59,477)( 60,480)( 61,475)( 62,474)( 63,473)( 64,476)( 65,433)( 66,436)( 67,435)( 68,434)( 69,437)( 70,440)( 71,439)( 72,438)( 73,427)( 74,426)( 75,425)( 76,428)( 77,431)( 78,430)( 79,429)( 80,432)( 81,417)( 82,420)( 83,419)( 84,418)( 85,421)( 86,424)( 87,423)( 88,422)( 89,447)( 90,446)( 91,445)( 92,448)( 93,443)( 94,442)( 95,441)( 96,444)( 97,305)( 98,308)( 99,307)(100,306)(101,309)(102,312)(103,311)(104,310)(105,299)(106,298)(107,297)(108,300)(109,303)(110,302)(111,301)(112,304)(113,289)(114,292)(115,291)(116,290)(117,293)(118,296)(119,295)(120,294)(121,319)(122,318)(123,317)(124,320)(125,315)(126,314)(127,313)(128,316)(129,369)(130,372)(131,371)(132,370)(133,373)(134,376)(135,375)(136,374)(137,363)(138,362)(139,361)(140,364)(141,367)(142,366)(143,365)(144,368)(145,353)(146,356)(147,355)(148,354)(149,357)(150,360)(151,359)(152,358)(153,383)(154,382)(155,381)(156,384)(157,379)(158,378)(159,377)(160,380)(161,337)(162,340)(163,339)(164,338)(165,341)(166,344)(167,343)(168,342)(169,331)(170,330)(171,329)(172,332)(173,335)(174,334)(175,333)(176,336)(177,321)(178,324)(179,323)(180,322)(181,325)(182,328)(183,327)(184,326)(185,351)(186,350)(187,349)(188,352)(189,347)(190,346)(191,345)(192,348)(193,561)(194,564)(195,563)(196,562)(197,565)(198,568)(199,567)(200,566)(201,555)(202,554)(203,553)(204,556)(205,559)(206,558)(207,557)(208,560)(209,545)(210,548)(211,547)(212,546)(213,549)(214,552)(215,551)(216,550)(217,575)(218,574)(219,573)(220,576)(221,571)(222,570)(223,569)(224,572)(225,529)(226,532)(227,531)(228,530)(229,533)(230,536)(231,535)(232,534)(233,523)(234,522)(235,521)(236,524)(237,527)(238,526)(239,525)(240,528)(241,513)(242,516)(243,515)(244,514)(245,517)(246,520)(247,519)(248,518)(249,543)(250,542)(251,541)(252,544)(253,539)(254,538)(255,537)(256,540)(257,497)(258,500)(259,499)(260,498)(261,501)(262,504)(263,503)(264,502)(265,491)(266,490)(267,489)(268,492)(269,495)(270,494)(271,493)(272,496)(273,481)(274,484)(275,483)(276,482)(277,485)(278,488)(279,487)(280,486)(281,511)(282,510)(283,509)(284,512)(285,507)(286,506)(287,505)(288,508);
poly := sub<Sym(576)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle