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}*1152d
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 : 18
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}*384d
   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 := (  1,405)(  2,408)(  3,407)(  4,406)(  5,401)(  6,404)(  7,403)(  8,402)(  9,399)( 10,398)( 11,397)( 12,400)( 13,395)( 14,394)( 15,393)( 16,396)( 17,389)( 18,392)( 19,391)( 20,390)( 21,385)( 22,388)( 23,387)( 24,386)( 25,411)( 26,410)( 27,409)( 28,412)( 29,415)( 30,414)( 31,413)( 32,416)( 33,469)( 34,472)( 35,471)( 36,470)( 37,465)( 38,468)( 39,467)( 40,466)( 41,463)( 42,462)( 43,461)( 44,464)( 45,459)( 46,458)( 47,457)( 48,460)( 49,453)( 50,456)( 51,455)( 52,454)( 53,449)( 54,452)( 55,451)( 56,450)( 57,475)( 58,474)( 59,473)( 60,476)( 61,479)( 62,478)( 63,477)( 64,480)( 65,437)( 66,440)( 67,439)( 68,438)( 69,433)( 70,436)( 71,435)( 72,434)( 73,431)( 74,430)( 75,429)( 76,432)( 77,427)( 78,426)( 79,425)( 80,428)( 81,421)( 82,424)( 83,423)( 84,422)( 85,417)( 86,420)( 87,419)( 88,418)( 89,443)( 90,442)( 91,441)( 92,444)( 93,447)( 94,446)( 95,445)( 96,448)( 97,309)( 98,312)( 99,311)(100,310)(101,305)(102,308)(103,307)(104,306)(105,303)(106,302)(107,301)(108,304)(109,299)(110,298)(111,297)(112,300)(113,293)(114,296)(115,295)(116,294)(117,289)(118,292)(119,291)(120,290)(121,315)(122,314)(123,313)(124,316)(125,319)(126,318)(127,317)(128,320)(129,373)(130,376)(131,375)(132,374)(133,369)(134,372)(135,371)(136,370)(137,367)(138,366)(139,365)(140,368)(141,363)(142,362)(143,361)(144,364)(145,357)(146,360)(147,359)(148,358)(149,353)(150,356)(151,355)(152,354)(153,379)(154,378)(155,377)(156,380)(157,383)(158,382)(159,381)(160,384)(161,341)(162,344)(163,343)(164,342)(165,337)(166,340)(167,339)(168,338)(169,335)(170,334)(171,333)(172,336)(173,331)(174,330)(175,329)(176,332)(177,325)(178,328)(179,327)(180,326)(181,321)(182,324)(183,323)(184,322)(185,347)(186,346)(187,345)(188,348)(189,351)(190,350)(191,349)(192,352)(193,565)(194,568)(195,567)(196,566)(197,561)(198,564)(199,563)(200,562)(201,559)(202,558)(203,557)(204,560)(205,555)(206,554)(207,553)(208,556)(209,549)(210,552)(211,551)(212,550)(213,545)(214,548)(215,547)(216,546)(217,571)(218,570)(219,569)(220,572)(221,575)(222,574)(223,573)(224,576)(225,533)(226,536)(227,535)(228,534)(229,529)(230,532)(231,531)(232,530)(233,527)(234,526)(235,525)(236,528)(237,523)(238,522)(239,521)(240,524)(241,517)(242,520)(243,519)(244,518)(245,513)(246,516)(247,515)(248,514)(249,539)(250,538)(251,537)(252,540)(253,543)(254,542)(255,541)(256,544)(257,501)(258,504)(259,503)(260,502)(261,497)(262,500)(263,499)(264,498)(265,495)(266,494)(267,493)(268,496)(269,491)(270,490)(271,489)(272,492)(273,485)(274,488)(275,487)(276,486)(277,481)(278,484)(279,483)(280,482)(281,507)(282,506)(283,505)(284,508)(285,511)(286,510)(287,509)(288,512);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2 ];;
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)!(  1,405)(  2,408)(  3,407)(  4,406)(  5,401)(  6,404)(  7,403)(  8,402)(  9,399)( 10,398)( 11,397)( 12,400)( 13,395)( 14,394)( 15,393)( 16,396)( 17,389)( 18,392)( 19,391)( 20,390)( 21,385)( 22,388)( 23,387)( 24,386)( 25,411)( 26,410)( 27,409)( 28,412)( 29,415)( 30,414)( 31,413)( 32,416)( 33,469)( 34,472)( 35,471)( 36,470)( 37,465)( 38,468)( 39,467)( 40,466)( 41,463)( 42,462)( 43,461)( 44,464)( 45,459)( 46,458)( 47,457)( 48,460)( 49,453)( 50,456)( 51,455)( 52,454)( 53,449)( 54,452)( 55,451)( 56,450)( 57,475)( 58,474)( 59,473)( 60,476)( 61,479)( 62,478)( 63,477)( 64,480)( 65,437)( 66,440)( 67,439)( 68,438)( 69,433)( 70,436)( 71,435)( 72,434)( 73,431)( 74,430)( 75,429)( 76,432)( 77,427)( 78,426)( 79,425)( 80,428)( 81,421)( 82,424)( 83,423)( 84,422)( 85,417)( 86,420)( 87,419)( 88,418)( 89,443)( 90,442)( 91,441)( 92,444)( 93,447)( 94,446)( 95,445)( 96,448)( 97,309)( 98,312)( 99,311)(100,310)(101,305)(102,308)(103,307)(104,306)(105,303)(106,302)(107,301)(108,304)(109,299)(110,298)(111,297)(112,300)(113,293)(114,296)(115,295)(116,294)(117,289)(118,292)(119,291)(120,290)(121,315)(122,314)(123,313)(124,316)(125,319)(126,318)(127,317)(128,320)(129,373)(130,376)(131,375)(132,374)(133,369)(134,372)(135,371)(136,370)(137,367)(138,366)(139,365)(140,368)(141,363)(142,362)(143,361)(144,364)(145,357)(146,360)(147,359)(148,358)(149,353)(150,356)(151,355)(152,354)(153,379)(154,378)(155,377)(156,380)(157,383)(158,382)(159,381)(160,384)(161,341)(162,344)(163,343)(164,342)(165,337)(166,340)(167,339)(168,338)(169,335)(170,334)(171,333)(172,336)(173,331)(174,330)(175,329)(176,332)(177,325)(178,328)(179,327)(180,326)(181,321)(182,324)(183,323)(184,322)(185,347)(186,346)(187,345)(188,348)(189,351)(190,350)(191,349)(192,352)(193,565)(194,568)(195,567)(196,566)(197,561)(198,564)(199,563)(200,562)(201,559)(202,558)(203,557)(204,560)(205,555)(206,554)(207,553)(208,556)(209,549)(210,552)(211,551)(212,550)(213,545)(214,548)(215,547)(216,546)(217,571)(218,570)(219,569)(220,572)(221,575)(222,574)(223,573)(224,576)(225,533)(226,536)(227,535)(228,534)(229,529)(230,532)(231,531)(232,530)(233,527)(234,526)(235,525)(236,528)(237,523)(238,522)(239,521)(240,524)(241,517)(242,520)(243,519)(244,518)(245,513)(246,516)(247,515)(248,514)(249,539)(250,538)(251,537)(252,540)(253,543)(254,542)(255,541)(256,544)(257,501)(258,504)(259,503)(260,502)(261,497)(262,500)(263,499)(264,498)(265,495)(266,494)(267,493)(268,496)(269,491)(270,490)(271,489)(272,492)(273,485)(274,488)(275,487)(276,486)(277,481)(278,484)(279,483)(280,482)(281,507)(282,506)(283,505)(284,508)(285,511)(286,510)(287,509)(288,512);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2 >;
References : None.
to this polytope

Twisty Puzzle