Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,3}

Atlas Canonical Name {12,3}*1152b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1152,157458)
Rank
3
Schläfli Type
{12,3}
Vertices, edges, …
192, 288, 48
Order of s0s1s2
24
Order of s0s1s2s1
12
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

12-fold

24-fold

32-fold

48-fold

96-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^3*(s2*(s1*s0)^2)^2*s1*s2*s1*s0*s1*s2> of order 2

24 facets

96 vertex figures

P/N, where N=<(s0*s1)^6> of order 2

32 facets

96 vertex figures

P/N, where N=<s1*s0*s2*(s1*s0)^2*s1*(s2*(s1*s0)^2)^2*s1*s2*s1> of order 2

24 facets

96 vertex figures

P/N, where N=<s0*s1*s0*s2*(s1*s0)^3*s2*s1*s0*s1> of order 3

16 facets

64 vertex figures

P/N, where N=<(s0*s1)^4> of order 3

24 facets

64 vertex figures

P/N, where N=<s0*s2*(s1*s0)^5*s1*s2, s1*s0*s2*(s1*s0)^5*s1*s2*s1> of order 4

20 facets

48 vertex figures

P/N, where N=<(s0*s1)^6, s1*(s2*(s1*s0)^2)^2*s2*s1*s0*s1*s2> of order 4

20 facets

48 vertex figures

P/N, where N=<(s0*s1)^2> of order 6

16 facets

32 vertex figures

P/N, where N=<(s0*s1)^4, s0*(s2*(s1*s0)^2)^2*s2*s1*s0*s1*s2> of order 6

12 facets

32 vertex figures

P/N, where N=<(s0*s1)^4, (s0*s1)^2*s2*(s1*s0)^5*s1*s2> of order 6

12 facets

32 vertex figures

P/N, where N=<(s0*s1)^4, s0*s2*(s1*s0)^5*s1*s2, s0*(s2*(s1*s0)^2)^2*s2*s1*s0*s1*s2> of order 12

10 facets

16 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle