Polytope of Type {32,18}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,18}*1152
Also Known As : {32,18|2}. if this polytope has another name.
Group : SmallGroup(1152,34504)
Rank : 3
Schlafli Type : {32,18}
Number of vertices, edges, etc : 32, 288, 18
Order of s0s1s2 : 288
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {16,18}*576
   3-fold quotients : {32,6}*384
   4-fold quotients : {8,18}*288
   6-fold quotients : {16,6}*192
   8-fold quotients : {4,18}*144a
   9-fold quotients : {32,2}*128
   12-fold quotients : {8,6}*96
   16-fold quotients : {2,18}*72
   18-fold quotients : {16,2}*64
   24-fold quotients : {4,6}*48a
   32-fold quotients : {2,9}*36
   36-fold quotients : {8,2}*32
   48-fold quotients : {2,6}*24
   72-fold quotients : {4,2}*16
   96-fold quotients : {2,3}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

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