Polytope of Type {2,6,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,24}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157570)
Rank : 4
Schlafli Type : {2,6,24}
Number of vertices, edges, etc : 2, 12, 144, 48
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
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 : {2,3,24}*576, {2,6,12}*576b
3-fold quotients : {2,6,8}*384b
4-fold quotients : {2,3,12}*288
6-fold quotients : {2,3,8}*192, {2,6,4}*192
8-fold quotients : {2,6,6}*144c
12-fold quotients : {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
16-fold quotients : {2,3,6}*72
24-fold quotients : {2,3,4}*48, {2,6,2}*48
48-fold quotients : {2,3,2}*24
72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,435)( 4,436)( 5,440)( 6,439)( 7,438)( 8,437)( 9,442)( 10,441)( 11,451)( 12,452)( 13,456)( 14,455)( 15,454)( 16,453)( 17,458)( 18,457)( 19,443)( 20,444)( 21,448)( 22,447)( 23,446)( 24,445)( 25,450)( 26,449)( 27,483)( 28,484)( 29,488)( 30,487)( 31,486)( 32,485)( 33,490)( 34,489)( 35,499)( 36,500)( 37,504)( 38,503)( 39,502)( 40,501)( 41,506)( 42,505)( 43,491)( 44,492)( 45,496)( 46,495)( 47,494)( 48,493)( 49,498)( 50,497)( 51,459)( 52,460)( 53,464)( 54,463)( 55,462)( 56,461)( 57,466)( 58,465)( 59,475)( 60,476)( 61,480)( 62,479)( 63,478)( 64,477)( 65,482)( 66,481)( 67,467)( 68,468)( 69,472)( 70,471)( 71,470)( 72,469)( 73,474)( 74,473)( 75,507)( 76,508)( 77,512)( 78,511)( 79,510)( 80,509)( 81,514)( 82,513)( 83,523)( 84,524)( 85,528)( 86,527)( 87,526)( 88,525)( 89,530)( 90,529)( 91,515)( 92,516)( 93,520)( 94,519)( 95,518)( 96,517)( 97,522)( 98,521)( 99,555)(100,556)(101,560)(102,559)(103,558)(104,557)(105,562)(106,561)(107,571)(108,572)(109,576)(110,575)(111,574)(112,573)(113,578)(114,577)(115,563)(116,564)(117,568)(118,567)(119,566)(120,565)(121,570)(122,569)(123,531)(124,532)(125,536)(126,535)(127,534)(128,533)(129,538)(130,537)(131,547)(132,548)(133,552)(134,551)(135,550)(136,549)(137,554)(138,553)(139,539)(140,540)(141,544)(142,543)(143,542)(144,541)(145,546)(146,545)(147,292)(148,291)(149,295)(150,296)(151,293)(152,294)(153,297)(154,298)(155,308)(156,307)(157,311)(158,312)(159,309)(160,310)(161,313)(162,314)(163,300)(164,299)(165,303)(166,304)(167,301)(168,302)(169,305)(170,306)(171,340)(172,339)(173,343)(174,344)(175,341)(176,342)(177,345)(178,346)(179,356)(180,355)(181,359)(182,360)(183,357)(184,358)(185,361)(186,362)(187,348)(188,347)(189,351)(190,352)(191,349)(192,350)(193,353)(194,354)(195,316)(196,315)(197,319)(198,320)(199,317)(200,318)(201,321)(202,322)(203,332)(204,331)(205,335)(206,336)(207,333)(208,334)(209,337)(210,338)(211,324)(212,323)(213,327)(214,328)(215,325)(216,326)(217,329)(218,330)(219,364)(220,363)(221,367)(222,368)(223,365)(224,366)(225,369)(226,370)(227,380)(228,379)(229,383)(230,384)(231,381)(232,382)(233,385)(234,386)(235,372)(236,371)(237,375)(238,376)(239,373)(240,374)(241,377)(242,378)(243,412)(244,411)(245,415)(246,416)(247,413)(248,414)(249,417)(250,418)(251,428)(252,427)(253,431)(254,432)(255,429)(256,430)(257,433)(258,434)(259,420)(260,419)(261,423)(262,424)(263,421)(264,422)(265,425)(266,426)(267,388)(268,387)(269,391)(270,392)(271,389)(272,390)(273,393)(274,394)(275,404)(276,403)(277,407)(278,408)(279,405)(280,406)(281,409)(282,410)(283,396)(284,395)(285,399)(286,400)(287,397)(288,398)(289,401)(290,402);;
s2 := ( 3,539)( 4,540)( 5,542)( 6,541)( 7,545)( 8,546)( 9,543)( 10,544)( 11,531)( 12,532)( 13,534)( 14,533)( 15,537)( 16,538)( 17,535)( 18,536)( 19,547)( 20,548)( 21,550)( 22,549)( 23,553)( 24,554)( 25,551)( 26,552)( 27,515)( 28,516)( 29,518)( 30,517)( 31,521)( 32,522)( 33,519)( 34,520)( 35,507)( 36,508)( 37,510)( 38,509)( 39,513)( 40,514)( 41,511)( 42,512)( 43,523)( 44,524)( 45,526)( 46,525)( 47,529)( 48,530)( 49,527)( 50,528)( 51,563)( 52,564)( 53,566)( 54,565)( 55,569)( 56,570)( 57,567)( 58,568)( 59,555)( 60,556)( 61,558)( 62,557)( 63,561)( 64,562)( 65,559)( 66,560)( 67,571)( 68,572)( 69,574)( 70,573)( 71,577)( 72,578)( 73,575)( 74,576)( 75,467)( 76,468)( 77,470)( 78,469)( 79,473)( 80,474)( 81,471)( 82,472)( 83,459)( 84,460)( 85,462)( 86,461)( 87,465)( 88,466)( 89,463)( 90,464)( 91,475)( 92,476)( 93,478)( 94,477)( 95,481)( 96,482)( 97,479)( 98,480)( 99,443)(100,444)(101,446)(102,445)(103,449)(104,450)(105,447)(106,448)(107,435)(108,436)(109,438)(110,437)(111,441)(112,442)(113,439)(114,440)(115,451)(116,452)(117,454)(118,453)(119,457)(120,458)(121,455)(122,456)(123,491)(124,492)(125,494)(126,493)(127,497)(128,498)(129,495)(130,496)(131,483)(132,484)(133,486)(134,485)(135,489)(136,490)(137,487)(138,488)(139,499)(140,500)(141,502)(142,501)(143,505)(144,506)(145,503)(146,504)(147,396)(148,395)(149,397)(150,398)(151,402)(152,401)(153,400)(154,399)(155,388)(156,387)(157,389)(158,390)(159,394)(160,393)(161,392)(162,391)(163,404)(164,403)(165,405)(166,406)(167,410)(168,409)(169,408)(170,407)(171,372)(172,371)(173,373)(174,374)(175,378)(176,377)(177,376)(178,375)(179,364)(180,363)(181,365)(182,366)(183,370)(184,369)(185,368)(186,367)(187,380)(188,379)(189,381)(190,382)(191,386)(192,385)(193,384)(194,383)(195,420)(196,419)(197,421)(198,422)(199,426)(200,425)(201,424)(202,423)(203,412)(204,411)(205,413)(206,414)(207,418)(208,417)(209,416)(210,415)(211,428)(212,427)(213,429)(214,430)(215,434)(216,433)(217,432)(218,431)(219,324)(220,323)(221,325)(222,326)(223,330)(224,329)(225,328)(226,327)(227,316)(228,315)(229,317)(230,318)(231,322)(232,321)(233,320)(234,319)(235,332)(236,331)(237,333)(238,334)(239,338)(240,337)(241,336)(242,335)(243,300)(244,299)(245,301)(246,302)(247,306)(248,305)(249,304)(250,303)(251,292)(252,291)(253,293)(254,294)(255,298)(256,297)(257,296)(258,295)(259,308)(260,307)(261,309)(262,310)(263,314)(264,313)(265,312)(266,311)(267,348)(268,347)(269,349)(270,350)(271,354)(272,353)(273,352)(274,351)(275,340)(276,339)(277,341)(278,342)(279,346)(280,345)(281,344)(282,343)(283,356)(284,355)(285,357)(286,358)(287,362)(288,361)(289,360)(290,359);;
s3 := ( 3,297)( 4,298)( 5,295)( 6,296)( 7,294)( 8,293)( 9,292)( 10,291)( 11,313)( 12,314)( 13,311)( 14,312)( 15,310)( 16,309)( 17,308)( 18,307)( 19,305)( 20,306)( 21,303)( 22,304)( 23,302)( 24,301)( 25,300)( 26,299)( 27,321)( 28,322)( 29,319)( 30,320)( 31,318)( 32,317)( 33,316)( 34,315)( 35,337)( 36,338)( 37,335)( 38,336)( 39,334)( 40,333)( 41,332)( 42,331)( 43,329)( 44,330)( 45,327)( 46,328)( 47,326)( 48,325)( 49,324)( 50,323)( 51,345)( 52,346)( 53,343)( 54,344)( 55,342)( 56,341)( 57,340)( 58,339)( 59,361)( 60,362)( 61,359)( 62,360)( 63,358)( 64,357)( 65,356)( 66,355)( 67,353)( 68,354)( 69,351)( 70,352)( 71,350)( 72,349)( 73,348)( 74,347)( 75,369)( 76,370)( 77,367)( 78,368)( 79,366)( 80,365)( 81,364)( 82,363)( 83,385)( 84,386)( 85,383)( 86,384)( 87,382)( 88,381)( 89,380)( 90,379)( 91,377)( 92,378)( 93,375)( 94,376)( 95,374)( 96,373)( 97,372)( 98,371)( 99,393)(100,394)(101,391)(102,392)(103,390)(104,389)(105,388)(106,387)(107,409)(108,410)(109,407)(110,408)(111,406)(112,405)(113,404)(114,403)(115,401)(116,402)(117,399)(118,400)(119,398)(120,397)(121,396)(122,395)(123,417)(124,418)(125,415)(126,416)(127,414)(128,413)(129,412)(130,411)(131,433)(132,434)(133,431)(134,432)(135,430)(136,429)(137,428)(138,427)(139,425)(140,426)(141,423)(142,424)(143,422)(144,421)(145,420)(146,419)(147,442)(148,441)(149,440)(150,439)(151,437)(152,438)(153,435)(154,436)(155,458)(156,457)(157,456)(158,455)(159,453)(160,454)(161,451)(162,452)(163,450)(164,449)(165,448)(166,447)(167,445)(168,446)(169,443)(170,444)(171,466)(172,465)(173,464)(174,463)(175,461)(176,462)(177,459)(178,460)(179,482)(180,481)(181,480)(182,479)(183,477)(184,478)(185,475)(186,476)(187,474)(188,473)(189,472)(190,471)(191,469)(192,470)(193,467)(194,468)(195,490)(196,489)(197,488)(198,487)(199,485)(200,486)(201,483)(202,484)(203,506)(204,505)(205,504)(206,503)(207,501)(208,502)(209,499)(210,500)(211,498)(212,497)(213,496)(214,495)(215,493)(216,494)(217,491)(218,492)(219,514)(220,513)(221,512)(222,511)(223,509)(224,510)(225,507)(226,508)(227,530)(228,529)(229,528)(230,527)(231,525)(232,526)(233,523)(234,524)(235,522)(236,521)(237,520)(238,519)(239,517)(240,518)(241,515)(242,516)(243,538)(244,537)(245,536)(246,535)(247,533)(248,534)(249,531)(250,532)(251,554)(252,553)(253,552)(254,551)(255,549)(256,550)(257,547)(258,548)(259,546)(260,545)(261,544)(262,543)(263,541)(264,542)(265,539)(266,540)(267,562)(268,561)(269,560)(270,559)(271,557)(272,558)(273,555)(274,556)(275,578)(276,577)(277,576)(278,575)(279,573)(280,574)(281,571)(282,572)(283,570)(284,569)(285,568)(286,567)(287,565)(288,566)(289,563)(290,564);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(578)!(1,2);
s1 := Sym(578)!( 3,435)( 4,436)( 5,440)( 6,439)( 7,438)( 8,437)( 9,442)( 10,441)( 11,451)( 12,452)( 13,456)( 14,455)( 15,454)( 16,453)( 17,458)( 18,457)( 19,443)( 20,444)( 21,448)( 22,447)( 23,446)( 24,445)( 25,450)( 26,449)( 27,483)( 28,484)( 29,488)( 30,487)( 31,486)( 32,485)( 33,490)( 34,489)( 35,499)( 36,500)( 37,504)( 38,503)( 39,502)( 40,501)( 41,506)( 42,505)( 43,491)( 44,492)( 45,496)( 46,495)( 47,494)( 48,493)( 49,498)( 50,497)( 51,459)( 52,460)( 53,464)( 54,463)( 55,462)( 56,461)( 57,466)( 58,465)( 59,475)( 60,476)( 61,480)( 62,479)( 63,478)( 64,477)( 65,482)( 66,481)( 67,467)( 68,468)( 69,472)( 70,471)( 71,470)( 72,469)( 73,474)( 74,473)( 75,507)( 76,508)( 77,512)( 78,511)( 79,510)( 80,509)( 81,514)( 82,513)( 83,523)( 84,524)( 85,528)( 86,527)( 87,526)( 88,525)( 89,530)( 90,529)( 91,515)( 92,516)( 93,520)( 94,519)( 95,518)( 96,517)( 97,522)( 98,521)( 99,555)(100,556)(101,560)(102,559)(103,558)(104,557)(105,562)(106,561)(107,571)(108,572)(109,576)(110,575)(111,574)(112,573)(113,578)(114,577)(115,563)(116,564)(117,568)(118,567)(119,566)(120,565)(121,570)(122,569)(123,531)(124,532)(125,536)(126,535)(127,534)(128,533)(129,538)(130,537)(131,547)(132,548)(133,552)(134,551)(135,550)(136,549)(137,554)(138,553)(139,539)(140,540)(141,544)(142,543)(143,542)(144,541)(145,546)(146,545)(147,292)(148,291)(149,295)(150,296)(151,293)(152,294)(153,297)(154,298)(155,308)(156,307)(157,311)(158,312)(159,309)(160,310)(161,313)(162,314)(163,300)(164,299)(165,303)(166,304)(167,301)(168,302)(169,305)(170,306)(171,340)(172,339)(173,343)(174,344)(175,341)(176,342)(177,345)(178,346)(179,356)(180,355)(181,359)(182,360)(183,357)(184,358)(185,361)(186,362)(187,348)(188,347)(189,351)(190,352)(191,349)(192,350)(193,353)(194,354)(195,316)(196,315)(197,319)(198,320)(199,317)(200,318)(201,321)(202,322)(203,332)(204,331)(205,335)(206,336)(207,333)(208,334)(209,337)(210,338)(211,324)(212,323)(213,327)(214,328)(215,325)(216,326)(217,329)(218,330)(219,364)(220,363)(221,367)(222,368)(223,365)(224,366)(225,369)(226,370)(227,380)(228,379)(229,383)(230,384)(231,381)(232,382)(233,385)(234,386)(235,372)(236,371)(237,375)(238,376)(239,373)(240,374)(241,377)(242,378)(243,412)(244,411)(245,415)(246,416)(247,413)(248,414)(249,417)(250,418)(251,428)(252,427)(253,431)(254,432)(255,429)(256,430)(257,433)(258,434)(259,420)(260,419)(261,423)(262,424)(263,421)(264,422)(265,425)(266,426)(267,388)(268,387)(269,391)(270,392)(271,389)(272,390)(273,393)(274,394)(275,404)(276,403)(277,407)(278,408)(279,405)(280,406)(281,409)(282,410)(283,396)(284,395)(285,399)(286,400)(287,397)(288,398)(289,401)(290,402);
s2 := Sym(578)!( 3,539)( 4,540)( 5,542)( 6,541)( 7,545)( 8,546)( 9,543)( 10,544)( 11,531)( 12,532)( 13,534)( 14,533)( 15,537)( 16,538)( 17,535)( 18,536)( 19,547)( 20,548)( 21,550)( 22,549)( 23,553)( 24,554)( 25,551)( 26,552)( 27,515)( 28,516)( 29,518)( 30,517)( 31,521)( 32,522)( 33,519)( 34,520)( 35,507)( 36,508)( 37,510)( 38,509)( 39,513)( 40,514)( 41,511)( 42,512)( 43,523)( 44,524)( 45,526)( 46,525)( 47,529)( 48,530)( 49,527)( 50,528)( 51,563)( 52,564)( 53,566)( 54,565)( 55,569)( 56,570)( 57,567)( 58,568)( 59,555)( 60,556)( 61,558)( 62,557)( 63,561)( 64,562)( 65,559)( 66,560)( 67,571)( 68,572)( 69,574)( 70,573)( 71,577)( 72,578)( 73,575)( 74,576)( 75,467)( 76,468)( 77,470)( 78,469)( 79,473)( 80,474)( 81,471)( 82,472)( 83,459)( 84,460)( 85,462)( 86,461)( 87,465)( 88,466)( 89,463)( 90,464)( 91,475)( 92,476)( 93,478)( 94,477)( 95,481)( 96,482)( 97,479)( 98,480)( 99,443)(100,444)(101,446)(102,445)(103,449)(104,450)(105,447)(106,448)(107,435)(108,436)(109,438)(110,437)(111,441)(112,442)(113,439)(114,440)(115,451)(116,452)(117,454)(118,453)(119,457)(120,458)(121,455)(122,456)(123,491)(124,492)(125,494)(126,493)(127,497)(128,498)(129,495)(130,496)(131,483)(132,484)(133,486)(134,485)(135,489)(136,490)(137,487)(138,488)(139,499)(140,500)(141,502)(142,501)(143,505)(144,506)(145,503)(146,504)(147,396)(148,395)(149,397)(150,398)(151,402)(152,401)(153,400)(154,399)(155,388)(156,387)(157,389)(158,390)(159,394)(160,393)(161,392)(162,391)(163,404)(164,403)(165,405)(166,406)(167,410)(168,409)(169,408)(170,407)(171,372)(172,371)(173,373)(174,374)(175,378)(176,377)(177,376)(178,375)(179,364)(180,363)(181,365)(182,366)(183,370)(184,369)(185,368)(186,367)(187,380)(188,379)(189,381)(190,382)(191,386)(192,385)(193,384)(194,383)(195,420)(196,419)(197,421)(198,422)(199,426)(200,425)(201,424)(202,423)(203,412)(204,411)(205,413)(206,414)(207,418)(208,417)(209,416)(210,415)(211,428)(212,427)(213,429)(214,430)(215,434)(216,433)(217,432)(218,431)(219,324)(220,323)(221,325)(222,326)(223,330)(224,329)(225,328)(226,327)(227,316)(228,315)(229,317)(230,318)(231,322)(232,321)(233,320)(234,319)(235,332)(236,331)(237,333)(238,334)(239,338)(240,337)(241,336)(242,335)(243,300)(244,299)(245,301)(246,302)(247,306)(248,305)(249,304)(250,303)(251,292)(252,291)(253,293)(254,294)(255,298)(256,297)(257,296)(258,295)(259,308)(260,307)(261,309)(262,310)(263,314)(264,313)(265,312)(266,311)(267,348)(268,347)(269,349)(270,350)(271,354)(272,353)(273,352)(274,351)(275,340)(276,339)(277,341)(278,342)(279,346)(280,345)(281,344)(282,343)(283,356)(284,355)(285,357)(286,358)(287,362)(288,361)(289,360)(290,359);
s3 := Sym(578)!( 3,297)( 4,298)( 5,295)( 6,296)( 7,294)( 8,293)( 9,292)( 10,291)( 11,313)( 12,314)( 13,311)( 14,312)( 15,310)( 16,309)( 17,308)( 18,307)( 19,305)( 20,306)( 21,303)( 22,304)( 23,302)( 24,301)( 25,300)( 26,299)( 27,321)( 28,322)( 29,319)( 30,320)( 31,318)( 32,317)( 33,316)( 34,315)( 35,337)( 36,338)( 37,335)( 38,336)( 39,334)( 40,333)( 41,332)( 42,331)( 43,329)( 44,330)( 45,327)( 46,328)( 47,326)( 48,325)( 49,324)( 50,323)( 51,345)( 52,346)( 53,343)( 54,344)( 55,342)( 56,341)( 57,340)( 58,339)( 59,361)( 60,362)( 61,359)( 62,360)( 63,358)( 64,357)( 65,356)( 66,355)( 67,353)( 68,354)( 69,351)( 70,352)( 71,350)( 72,349)( 73,348)( 74,347)( 75,369)( 76,370)( 77,367)( 78,368)( 79,366)( 80,365)( 81,364)( 82,363)( 83,385)( 84,386)( 85,383)( 86,384)( 87,382)( 88,381)( 89,380)( 90,379)( 91,377)( 92,378)( 93,375)( 94,376)( 95,374)( 96,373)( 97,372)( 98,371)( 99,393)(100,394)(101,391)(102,392)(103,390)(104,389)(105,388)(106,387)(107,409)(108,410)(109,407)(110,408)(111,406)(112,405)(113,404)(114,403)(115,401)(116,402)(117,399)(118,400)(119,398)(120,397)(121,396)(122,395)(123,417)(124,418)(125,415)(126,416)(127,414)(128,413)(129,412)(130,411)(131,433)(132,434)(133,431)(134,432)(135,430)(136,429)(137,428)(138,427)(139,425)(140,426)(141,423)(142,424)(143,422)(144,421)(145,420)(146,419)(147,442)(148,441)(149,440)(150,439)(151,437)(152,438)(153,435)(154,436)(155,458)(156,457)(157,456)(158,455)(159,453)(160,454)(161,451)(162,452)(163,450)(164,449)(165,448)(166,447)(167,445)(168,446)(169,443)(170,444)(171,466)(172,465)(173,464)(174,463)(175,461)(176,462)(177,459)(178,460)(179,482)(180,481)(181,480)(182,479)(183,477)(184,478)(185,475)(186,476)(187,474)(188,473)(189,472)(190,471)(191,469)(192,470)(193,467)(194,468)(195,490)(196,489)(197,488)(198,487)(199,485)(200,486)(201,483)(202,484)(203,506)(204,505)(205,504)(206,503)(207,501)(208,502)(209,499)(210,500)(211,498)(212,497)(213,496)(214,495)(215,493)(216,494)(217,491)(218,492)(219,514)(220,513)(221,512)(222,511)(223,509)(224,510)(225,507)(226,508)(227,530)(228,529)(229,528)(230,527)(231,525)(232,526)(233,523)(234,524)(235,522)(236,521)(237,520)(238,519)(239,517)(240,518)(241,515)(242,516)(243,538)(244,537)(245,536)(246,535)(247,533)(248,534)(249,531)(250,532)(251,554)(252,553)(253,552)(254,551)(255,549)(256,550)(257,547)(258,548)(259,546)(260,545)(261,544)(262,543)(263,541)(264,542)(265,539)(266,540)(267,562)(268,561)(269,560)(270,559)(271,557)(272,558)(273,555)(274,556)(275,578)(276,577)(277,576)(278,575)(279,573)(280,574)(281,571)(282,572)(283,570)(284,569)(285,568)(286,567)(287,565)(288,566)(289,563)(290,564);
poly := sub<Sym(578)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >;
to this polytope