Polytope of Type {12,3,4} with group SmallGroup(1152,157458)

Overview

Group: SmallGroup(1152,157458)
Rank: 4
Schläfli Type: {12,3,4}
Vertices, edges, …: 48, 72, 24, 4
Order of s₀s₁s₂s₃: 24
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

2-fold

{6,3,4}*576

8-fold

{6,3,4}*144

24-fold

{2,3,4}*48

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)^4> of order 3

4 facets

4 of 3-fold non-regular quotient of {12,3}*288

16 vertex figures

16 of {3,4}*24

Representations

Permutation Representation (GAP)

s0 := (  3,  4)(  5,  7)(  6,  8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 43, 44)( 45, 47)( 46, 48)( 51, 52)( 53, 55)( 54, 56)( 59, 60)( 61, 63)( 62, 64)( 67, 68)( 69, 71)( 70, 72)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)( 91, 92)( 93, 95)( 94, 96)( 97,193)( 98,194)( 99,196)(100,195)(101,199)(102,200)(103,197)(104,198)(105,201)(106,202)(107,204)(108,203)(109,207)(110,208)(111,205)(112,206)(113,209)(114,210)(115,212)(116,211)(117,215)(118,216)(119,213)(120,214)(121,217)(122,218)(123,220)(124,219)(125,223)(126,224)(127,221)(128,222)(129,225)(130,226)(131,228)(132,227)(133,231)(134,232)(135,229)(136,230)(137,233)(138,234)(139,236)(140,235)(141,239)(142,240)(143,237)(144,238)(145,241)(146,242)(147,244)(148,243)(149,247)(150,248)(151,245)(152,246)(153,249)(154,250)(155,252)(156,251)(157,255)(158,256)(159,253)(160,254)(161,257)(162,258)(163,260)(164,259)(165,263)(166,264)(167,261)(168,262)(169,265)(170,266)(171,268)(172,267)(173,271)(174,272)(175,269)(176,270)(177,273)(178,274)(179,276)(180,275)(181,279)(182,280)(183,277)(184,278)(185,281)(186,282)(187,284)(188,283)(189,287)(190,288)(191,285)(192,286)(289,290)(293,296)(294,295)(297,298)(301,304)(302,303)(305,306)(309,312)(310,311)(313,314)(317,320)(318,319)(321,322)(325,328)(326,327)(329,330)(333,336)(334,335)(337,338)(341,344)(342,343)(345,346)(349,352)(350,351)(353,354)(357,360)(358,359)(361,362)(365,368)(366,367)(369,370)(373,376)(374,375)(377,378)(381,384)(382,383)(385,482)(386,481)(387,483)(388,484)(389,488)(390,487)(391,486)(392,485)(393,490)(394,489)(395,491)(396,492)(397,496)(398,495)(399,494)(400,493)(401,498)(402,497)(403,499)(404,500)(405,504)(406,503)(407,502)(408,501)(409,506)(410,505)(411,507)(412,508)(413,512)(414,511)(415,510)(416,509)(417,514)(418,513)(419,515)(420,516)(421,520)(422,519)(423,518)(424,517)(425,522)(426,521)(427,523)(428,524)(429,528)(430,527)(431,526)(432,525)(433,530)(434,529)(435,531)(436,532)(437,536)(438,535)(439,534)(440,533)(441,538)(442,537)(443,539)(444,540)(445,544)(446,543)(447,542)(448,541)(449,546)(450,545)(451,547)(452,548)(453,552)(454,551)(455,550)(456,549)(457,554)(458,553)(459,555)(460,556)(461,560)(462,559)(463,558)(464,557)(465,562)(466,561)(467,563)(468,564)(469,568)(470,567)(471,566)(472,565)(473,570)(474,569)(475,571)(476,572)(477,576)(478,575)(479,574)(480,573);;
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);;
s3 := (  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432)(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)(440,448)(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)(456,464)(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)(472,480)(481,489)(482,490)(483,491)(484,492)(485,493)(486,494)(487,495)(488,496)(497,505)(498,506)(499,507)(500,508)(501,509)(502,510)(503,511)(504,512)(513,521)(514,522)(515,523)(516,524)(517,525)(518,526)(519,527)(520,528)(529,537)(530,538)(531,539)(532,540)(533,541)(534,542)(535,543)(536,544)(545,553)(546,554)(547,555)(548,556)(549,557)(550,558)(551,559)(552,560)(561,569)(562,570)(563,571)(564,572)(565,573)(566,574)(567,575)(568,576);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(576)!(  3,  4)(  5,  7)(  6,  8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 43, 44)( 45, 47)( 46, 48)( 51, 52)( 53, 55)( 54, 56)( 59, 60)( 61, 63)( 62, 64)( 67, 68)( 69, 71)( 70, 72)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)( 91, 92)( 93, 95)( 94, 96)( 97,193)( 98,194)( 99,196)(100,195)(101,199)(102,200)(103,197)(104,198)(105,201)(106,202)(107,204)(108,203)(109,207)(110,208)(111,205)(112,206)(113,209)(114,210)(115,212)(116,211)(117,215)(118,216)(119,213)(120,214)(121,217)(122,218)(123,220)(124,219)(125,223)(126,224)(127,221)(128,222)(129,225)(130,226)(131,228)(132,227)(133,231)(134,232)(135,229)(136,230)(137,233)(138,234)(139,236)(140,235)(141,239)(142,240)(143,237)(144,238)(145,241)(146,242)(147,244)(148,243)(149,247)(150,248)(151,245)(152,246)(153,249)(154,250)(155,252)(156,251)(157,255)(158,256)(159,253)(160,254)(161,257)(162,258)(163,260)(164,259)(165,263)(166,264)(167,261)(168,262)(169,265)(170,266)(171,268)(172,267)(173,271)(174,272)(175,269)(176,270)(177,273)(178,274)(179,276)(180,275)(181,279)(182,280)(183,277)(184,278)(185,281)(186,282)(187,284)(188,283)(189,287)(190,288)(191,285)(192,286)(289,290)(293,296)(294,295)(297,298)(301,304)(302,303)(305,306)(309,312)(310,311)(313,314)(317,320)(318,319)(321,322)(325,328)(326,327)(329,330)(333,336)(334,335)(337,338)(341,344)(342,343)(345,346)(349,352)(350,351)(353,354)(357,360)(358,359)(361,362)(365,368)(366,367)(369,370)(373,376)(374,375)(377,378)(381,384)(382,383)(385,482)(386,481)(387,483)(388,484)(389,488)(390,487)(391,486)(392,485)(393,490)(394,489)(395,491)(396,492)(397,496)(398,495)(399,494)(400,493)(401,498)(402,497)(403,499)(404,500)(405,504)(406,503)(407,502)(408,501)(409,506)(410,505)(411,507)(412,508)(413,512)(414,511)(415,510)(416,509)(417,514)(418,513)(419,515)(420,516)(421,520)(422,519)(423,518)(424,517)(425,522)(426,521)(427,523)(428,524)(429,528)(430,527)(431,526)(432,525)(433,530)(434,529)(435,531)(436,532)(437,536)(438,535)(439,534)(440,533)(441,538)(442,537)(443,539)(444,540)(445,544)(446,543)(447,542)(448,541)(449,546)(450,545)(451,547)(452,548)(453,552)(454,551)(455,550)(456,549)(457,554)(458,553)(459,555)(460,556)(461,560)(462,559)(463,558)(464,557)(465,562)(466,561)(467,563)(468,564)(469,568)(470,567)(471,566)(472,565)(473,570)(474,569)(475,571)(476,572)(477,576)(478,575)(479,574)(480,573);
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);
s3 := Sym(576)!(  1,  9)(  2, 10)(  3, 11)(  4, 12)(  5, 13)(  6, 14)(  7, 15)(  8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144)(145,153)(146,154)(147,155)(148,156)(149,157)(150,158)(151,159)(152,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(177,185)(178,186)(179,187)(180,188)(181,189)(182,190)(183,191)(184,192)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)(209,217)(210,218)(211,219)(212,220)(213,221)(214,222)(215,223)(216,224)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)(241,249)(242,250)(243,251)(244,252)(245,253)(246,254)(247,255)(248,256)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)(273,281)(274,282)(275,283)(276,284)(277,285)(278,286)(279,287)(280,288)(289,297)(290,298)(291,299)(292,300)(293,301)(294,302)(295,303)(296,304)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320)(321,329)(322,330)(323,331)(324,332)(325,333)(326,334)(327,335)(328,336)(337,345)(338,346)(339,347)(340,348)(341,349)(342,350)(343,351)(344,352)(353,361)(354,362)(355,363)(356,364)(357,365)(358,366)(359,367)(360,368)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)(385,393)(386,394)(387,395)(388,396)(389,397)(390,398)(391,399)(392,400)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416)(417,425)(418,426)(419,427)(420,428)(421,429)(422,430)(423,431)(424,432)(433,441)(434,442)(435,443)(436,444)(437,445)(438,446)(439,447)(440,448)(449,457)(450,458)(451,459)(452,460)(453,461)(454,462)(455,463)(456,464)(465,473)(466,474)(467,475)(468,476)(469,477)(470,478)(471,479)(472,480)(481,489)(482,490)(483,491)(484,492)(485,493)(486,494)(487,495)(488,496)(497,505)(498,506)(499,507)(500,508)(501,509)(502,510)(503,511)(504,512)(513,521)(514,522)(515,523)(516,524)(517,525)(518,526)(519,527)(520,528)(529,537)(530,538)(531,539)(532,540)(533,541)(534,542)(535,543)(536,544)(545,553)(546,554)(547,555)(548,556)(549,557)(550,558)(551,559)(552,560)(561,569)(562,570)(563,571)(564,572)(565,573)(566,574)(567,575)(568,576);
poly := sub<Sym(576)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s3*s2*s1*s3*s2*s1*s3*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 >;

References

None.

to this polytope.