Part of the Atlas of Small Regular Polytopes

Polytope of Type {2,8,4,14}

Atlas Canonical Name {2,8,4,14}*1792b

Overview

Group
SmallGroup(1792,1036167)
Rank
5
Schläfli Type
{2,8,4,14}
Vertices, edges, …
2, 8, 16, 28, 14
Order of s0s1s2s3s4
56
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

7-fold

8-fold

14-fold

16-fold

28-fold

56-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := (1,2);;
s1 := (  3,227)(  4,228)(  5,229)(  6,230)(  7,231)(  8,232)(  9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,253)( 23,254)( 24,241)( 25,242)( 26,243)( 27,244)( 28,245)( 29,246)( 30,247)( 31,262)( 32,263)( 33,264)( 34,265)( 35,266)( 36,267)( 37,268)( 38,255)( 39,256)( 40,257)( 41,258)( 42,259)( 43,260)( 44,261)( 45,269)( 46,270)( 47,271)( 48,272)( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)( 57,281)( 58,282)( 59,283)( 60,284)( 61,285)( 62,286)( 63,287)( 64,288)( 65,289)( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,295)( 72,296)( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,309)( 79,310)( 80,297)( 81,298)( 82,299)( 83,300)( 84,301)( 85,302)( 86,303)( 87,318)( 88,319)( 89,320)( 90,321)( 91,322)( 92,323)( 93,324)( 94,311)( 95,312)( 96,313)( 97,314)( 98,315)( 99,316)(100,317)(101,325)(102,326)(103,327)(104,328)(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)(112,336)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)(129,360)(130,361)(131,362)(132,363)(133,364)(134,365)(135,366)(136,353)(137,354)(138,355)(139,356)(140,357)(141,358)(142,359)(143,374)(144,375)(145,376)(146,377)(147,378)(148,379)(149,380)(150,367)(151,368)(152,369)(153,370)(154,371)(155,372)(156,373)(157,381)(158,382)(159,383)(160,384)(161,385)(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)(169,393)(170,394)(171,395)(172,396)(173,397)(174,398)(175,399)(176,400)(177,401)(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)(184,408)(185,416)(186,417)(187,418)(188,419)(189,420)(190,421)(191,422)(192,409)(193,410)(194,411)(195,412)(196,413)(197,414)(198,415)(199,430)(200,431)(201,432)(202,433)(203,434)(204,435)(205,436)(206,423)(207,424)(208,425)(209,426)(210,427)(211,428)(212,429)(213,437)(214,438)(215,439)(216,440)(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)(224,448)(225,449)(226,450);;
s2 := ( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 36, 43)( 37, 44)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 50, 57)( 51, 58)( 87, 94)( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 92, 99)( 93,100)(101,108)(102,109)(103,110)(104,111)(105,112)(106,113)(107,114)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(127,141)(128,142)(143,164)(144,165)(145,166)(146,167)(147,168)(148,169)(149,170)(150,157)(151,158)(152,159)(153,160)(154,161)(155,162)(156,163)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(183,197)(184,198)(199,220)(200,221)(201,222)(202,223)(203,224)(204,225)(205,226)(206,213)(207,214)(208,215)(209,216)(210,217)(211,218)(212,219)(227,255)(228,256)(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,267)(240,268)(241,269)(242,270)(243,271)(244,272)(245,273)(246,274)(247,275)(248,276)(249,277)(250,278)(251,279)(252,280)(253,281)(254,282)(283,311)(284,312)(285,313)(286,314)(287,315)(288,316)(289,317)(290,318)(291,319)(292,320)(293,321)(294,322)(295,323)(296,324)(297,325)(298,326)(299,327)(300,328)(301,329)(302,330)(303,331)(304,332)(305,333)(306,334)(307,335)(308,336)(309,337)(310,338)(339,388)(340,389)(341,390)(342,391)(343,392)(344,393)(345,394)(346,381)(347,382)(348,383)(349,384)(350,385)(351,386)(352,387)(353,374)(354,375)(355,376)(356,377)(357,378)(358,379)(359,380)(360,367)(361,368)(362,369)(363,370)(364,371)(365,372)(366,373)(395,444)(396,445)(397,446)(398,447)(399,448)(400,449)(401,450)(402,437)(403,438)(404,439)(405,440)(406,441)(407,442)(408,443)(409,430)(410,431)(411,432)(412,433)(413,434)(414,435)(415,436)(416,423)(417,424)(418,425)(419,426)(420,427)(421,428)(422,429);;
s3 := (  3,171)(  4,177)(  5,176)(  6,175)(  7,174)(  8,173)(  9,172)( 10,178)( 11,184)( 12,183)( 13,182)( 14,181)( 15,180)( 16,179)( 17,185)( 18,191)( 19,190)( 20,189)( 21,188)( 22,187)( 23,186)( 24,192)( 25,198)( 26,197)( 27,196)( 28,195)( 29,194)( 30,193)( 31,206)( 32,212)( 33,211)( 34,210)( 35,209)( 36,208)( 37,207)( 38,199)( 39,205)( 40,204)( 41,203)( 42,202)( 43,201)( 44,200)( 45,220)( 46,226)( 47,225)( 48,224)( 49,223)( 50,222)( 51,221)( 52,213)( 53,219)( 54,218)( 55,217)( 56,216)( 57,215)( 58,214)( 59,115)( 60,121)( 61,120)( 62,119)( 63,118)( 64,117)( 65,116)( 66,122)( 67,128)( 68,127)( 69,126)( 70,125)( 71,124)( 72,123)( 73,129)( 74,135)( 75,134)( 76,133)( 77,132)( 78,131)( 79,130)( 80,136)( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,137)( 87,150)( 88,156)( 89,155)( 90,154)( 91,153)( 92,152)( 93,151)( 94,143)( 95,149)( 96,148)( 97,147)( 98,146)( 99,145)(100,144)(101,164)(102,170)(103,169)(104,168)(105,167)(106,166)(107,165)(108,157)(109,163)(110,162)(111,161)(112,160)(113,159)(114,158)(227,395)(228,401)(229,400)(230,399)(231,398)(232,397)(233,396)(234,402)(235,408)(236,407)(237,406)(238,405)(239,404)(240,403)(241,409)(242,415)(243,414)(244,413)(245,412)(246,411)(247,410)(248,416)(249,422)(250,421)(251,420)(252,419)(253,418)(254,417)(255,430)(256,436)(257,435)(258,434)(259,433)(260,432)(261,431)(262,423)(263,429)(264,428)(265,427)(266,426)(267,425)(268,424)(269,444)(270,450)(271,449)(272,448)(273,447)(274,446)(275,445)(276,437)(277,443)(278,442)(279,441)(280,440)(281,439)(282,438)(283,339)(284,345)(285,344)(286,343)(287,342)(288,341)(289,340)(290,346)(291,352)(292,351)(293,350)(294,349)(295,348)(296,347)(297,353)(298,359)(299,358)(300,357)(301,356)(302,355)(303,354)(304,360)(305,366)(306,365)(307,364)(308,363)(309,362)(310,361)(311,374)(312,380)(313,379)(314,378)(315,377)(316,376)(317,375)(318,367)(319,373)(320,372)(321,371)(322,370)(323,369)(324,368)(325,388)(326,394)(327,393)(328,392)(329,391)(330,390)(331,389)(332,381)(333,387)(334,386)(335,385)(336,384)(337,383)(338,382);;
s4 := (  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)( 10, 67)( 11, 66)( 12, 72)( 13, 71)( 14, 70)( 15, 69)( 16, 68)( 17, 74)( 18, 73)( 19, 79)( 20, 78)( 21, 77)( 22, 76)( 23, 75)( 24, 81)( 25, 80)( 26, 86)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 88)( 32, 87)( 33, 93)( 34, 92)( 35, 91)( 36, 90)( 37, 89)( 38, 95)( 39, 94)( 40,100)( 41, 99)( 42, 98)( 43, 97)( 44, 96)( 45,102)( 46,101)( 47,107)( 48,106)( 49,105)( 50,104)( 51,103)( 52,109)( 53,108)( 54,114)( 55,113)( 56,112)( 57,111)( 58,110)(115,172)(116,171)(117,177)(118,176)(119,175)(120,174)(121,173)(122,179)(123,178)(124,184)(125,183)(126,182)(127,181)(128,180)(129,186)(130,185)(131,191)(132,190)(133,189)(134,188)(135,187)(136,193)(137,192)(138,198)(139,197)(140,196)(141,195)(142,194)(143,200)(144,199)(145,205)(146,204)(147,203)(148,202)(149,201)(150,207)(151,206)(152,212)(153,211)(154,210)(155,209)(156,208)(157,214)(158,213)(159,219)(160,218)(161,217)(162,216)(163,215)(164,221)(165,220)(166,226)(167,225)(168,224)(169,223)(170,222)(227,284)(228,283)(229,289)(230,288)(231,287)(232,286)(233,285)(234,291)(235,290)(236,296)(237,295)(238,294)(239,293)(240,292)(241,298)(242,297)(243,303)(244,302)(245,301)(246,300)(247,299)(248,305)(249,304)(250,310)(251,309)(252,308)(253,307)(254,306)(255,312)(256,311)(257,317)(258,316)(259,315)(260,314)(261,313)(262,319)(263,318)(264,324)(265,323)(266,322)(267,321)(268,320)(269,326)(270,325)(271,331)(272,330)(273,329)(274,328)(275,327)(276,333)(277,332)(278,338)(279,337)(280,336)(281,335)(282,334)(339,396)(340,395)(341,401)(342,400)(343,399)(344,398)(345,397)(346,403)(347,402)(348,408)(349,407)(350,406)(351,405)(352,404)(353,410)(354,409)(355,415)(356,414)(357,413)(358,412)(359,411)(360,417)(361,416)(362,422)(363,421)(364,420)(365,419)(366,418)(367,424)(368,423)(369,429)(370,428)(371,427)(372,426)(373,425)(374,431)(375,430)(376,436)(377,435)(378,434)(379,433)(380,432)(381,438)(382,437)(383,443)(384,442)(385,441)(386,440)(387,439)(388,445)(389,444)(390,450)(391,449)(392,448)(393,447)(394,446);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(450)!(1,2);
s1 := Sym(450)!(  3,227)(  4,228)(  5,229)(  6,230)(  7,231)(  8,232)(  9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,253)( 23,254)( 24,241)( 25,242)( 26,243)( 27,244)( 28,245)( 29,246)( 30,247)( 31,262)( 32,263)( 33,264)( 34,265)( 35,266)( 36,267)( 37,268)( 38,255)( 39,256)( 40,257)( 41,258)( 42,259)( 43,260)( 44,261)( 45,269)( 46,270)( 47,271)( 48,272)( 49,273)( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)( 57,281)( 58,282)( 59,283)( 60,284)( 61,285)( 62,286)( 63,287)( 64,288)( 65,289)( 66,290)( 67,291)( 68,292)( 69,293)( 70,294)( 71,295)( 72,296)( 73,304)( 74,305)( 75,306)( 76,307)( 77,308)( 78,309)( 79,310)( 80,297)( 81,298)( 82,299)( 83,300)( 84,301)( 85,302)( 86,303)( 87,318)( 88,319)( 89,320)( 90,321)( 91,322)( 92,323)( 93,324)( 94,311)( 95,312)( 96,313)( 97,314)( 98,315)( 99,316)(100,317)(101,325)(102,326)(103,327)(104,328)(105,329)(106,330)(107,331)(108,332)(109,333)(110,334)(111,335)(112,336)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)(129,360)(130,361)(131,362)(132,363)(133,364)(134,365)(135,366)(136,353)(137,354)(138,355)(139,356)(140,357)(141,358)(142,359)(143,374)(144,375)(145,376)(146,377)(147,378)(148,379)(149,380)(150,367)(151,368)(152,369)(153,370)(154,371)(155,372)(156,373)(157,381)(158,382)(159,383)(160,384)(161,385)(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)(169,393)(170,394)(171,395)(172,396)(173,397)(174,398)(175,399)(176,400)(177,401)(178,402)(179,403)(180,404)(181,405)(182,406)(183,407)(184,408)(185,416)(186,417)(187,418)(188,419)(189,420)(190,421)(191,422)(192,409)(193,410)(194,411)(195,412)(196,413)(197,414)(198,415)(199,430)(200,431)(201,432)(202,433)(203,434)(204,435)(205,436)(206,423)(207,424)(208,425)(209,426)(210,427)(211,428)(212,429)(213,437)(214,438)(215,439)(216,440)(217,441)(218,442)(219,443)(220,444)(221,445)(222,446)(223,447)(224,448)(225,449)(226,450);
s2 := Sym(450)!( 31, 38)( 32, 39)( 33, 40)( 34, 41)( 35, 42)( 36, 43)( 37, 44)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 50, 57)( 51, 58)( 87, 94)( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 92, 99)( 93,100)(101,108)(102,109)(103,110)(104,111)(105,112)(106,113)(107,114)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(127,141)(128,142)(143,164)(144,165)(145,166)(146,167)(147,168)(148,169)(149,170)(150,157)(151,158)(152,159)(153,160)(154,161)(155,162)(156,163)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(183,197)(184,198)(199,220)(200,221)(201,222)(202,223)(203,224)(204,225)(205,226)(206,213)(207,214)(208,215)(209,216)(210,217)(211,218)(212,219)(227,255)(228,256)(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,267)(240,268)(241,269)(242,270)(243,271)(244,272)(245,273)(246,274)(247,275)(248,276)(249,277)(250,278)(251,279)(252,280)(253,281)(254,282)(283,311)(284,312)(285,313)(286,314)(287,315)(288,316)(289,317)(290,318)(291,319)(292,320)(293,321)(294,322)(295,323)(296,324)(297,325)(298,326)(299,327)(300,328)(301,329)(302,330)(303,331)(304,332)(305,333)(306,334)(307,335)(308,336)(309,337)(310,338)(339,388)(340,389)(341,390)(342,391)(343,392)(344,393)(345,394)(346,381)(347,382)(348,383)(349,384)(350,385)(351,386)(352,387)(353,374)(354,375)(355,376)(356,377)(357,378)(358,379)(359,380)(360,367)(361,368)(362,369)(363,370)(364,371)(365,372)(366,373)(395,444)(396,445)(397,446)(398,447)(399,448)(400,449)(401,450)(402,437)(403,438)(404,439)(405,440)(406,441)(407,442)(408,443)(409,430)(410,431)(411,432)(412,433)(413,434)(414,435)(415,436)(416,423)(417,424)(418,425)(419,426)(420,427)(421,428)(422,429);
s3 := Sym(450)!(  3,171)(  4,177)(  5,176)(  6,175)(  7,174)(  8,173)(  9,172)( 10,178)( 11,184)( 12,183)( 13,182)( 14,181)( 15,180)( 16,179)( 17,185)( 18,191)( 19,190)( 20,189)( 21,188)( 22,187)( 23,186)( 24,192)( 25,198)( 26,197)( 27,196)( 28,195)( 29,194)( 30,193)( 31,206)( 32,212)( 33,211)( 34,210)( 35,209)( 36,208)( 37,207)( 38,199)( 39,205)( 40,204)( 41,203)( 42,202)( 43,201)( 44,200)( 45,220)( 46,226)( 47,225)( 48,224)( 49,223)( 50,222)( 51,221)( 52,213)( 53,219)( 54,218)( 55,217)( 56,216)( 57,215)( 58,214)( 59,115)( 60,121)( 61,120)( 62,119)( 63,118)( 64,117)( 65,116)( 66,122)( 67,128)( 68,127)( 69,126)( 70,125)( 71,124)( 72,123)( 73,129)( 74,135)( 75,134)( 76,133)( 77,132)( 78,131)( 79,130)( 80,136)( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,137)( 87,150)( 88,156)( 89,155)( 90,154)( 91,153)( 92,152)( 93,151)( 94,143)( 95,149)( 96,148)( 97,147)( 98,146)( 99,145)(100,144)(101,164)(102,170)(103,169)(104,168)(105,167)(106,166)(107,165)(108,157)(109,163)(110,162)(111,161)(112,160)(113,159)(114,158)(227,395)(228,401)(229,400)(230,399)(231,398)(232,397)(233,396)(234,402)(235,408)(236,407)(237,406)(238,405)(239,404)(240,403)(241,409)(242,415)(243,414)(244,413)(245,412)(246,411)(247,410)(248,416)(249,422)(250,421)(251,420)(252,419)(253,418)(254,417)(255,430)(256,436)(257,435)(258,434)(259,433)(260,432)(261,431)(262,423)(263,429)(264,428)(265,427)(266,426)(267,425)(268,424)(269,444)(270,450)(271,449)(272,448)(273,447)(274,446)(275,445)(276,437)(277,443)(278,442)(279,441)(280,440)(281,439)(282,438)(283,339)(284,345)(285,344)(286,343)(287,342)(288,341)(289,340)(290,346)(291,352)(292,351)(293,350)(294,349)(295,348)(296,347)(297,353)(298,359)(299,358)(300,357)(301,356)(302,355)(303,354)(304,360)(305,366)(306,365)(307,364)(308,363)(309,362)(310,361)(311,374)(312,380)(313,379)(314,378)(315,377)(316,376)(317,375)(318,367)(319,373)(320,372)(321,371)(322,370)(323,369)(324,368)(325,388)(326,394)(327,393)(328,392)(329,391)(330,390)(331,389)(332,381)(333,387)(334,386)(335,385)(336,384)(337,383)(338,382);
s4 := Sym(450)!(  3, 60)(  4, 59)(  5, 65)(  6, 64)(  7, 63)(  8, 62)(  9, 61)( 10, 67)( 11, 66)( 12, 72)( 13, 71)( 14, 70)( 15, 69)( 16, 68)( 17, 74)( 18, 73)( 19, 79)( 20, 78)( 21, 77)( 22, 76)( 23, 75)( 24, 81)( 25, 80)( 26, 86)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 88)( 32, 87)( 33, 93)( 34, 92)( 35, 91)( 36, 90)( 37, 89)( 38, 95)( 39, 94)( 40,100)( 41, 99)( 42, 98)( 43, 97)( 44, 96)( 45,102)( 46,101)( 47,107)( 48,106)( 49,105)( 50,104)( 51,103)( 52,109)( 53,108)( 54,114)( 55,113)( 56,112)( 57,111)( 58,110)(115,172)(116,171)(117,177)(118,176)(119,175)(120,174)(121,173)(122,179)(123,178)(124,184)(125,183)(126,182)(127,181)(128,180)(129,186)(130,185)(131,191)(132,190)(133,189)(134,188)(135,187)(136,193)(137,192)(138,198)(139,197)(140,196)(141,195)(142,194)(143,200)(144,199)(145,205)(146,204)(147,203)(148,202)(149,201)(150,207)(151,206)(152,212)(153,211)(154,210)(155,209)(156,208)(157,214)(158,213)(159,219)(160,218)(161,217)(162,216)(163,215)(164,221)(165,220)(166,226)(167,225)(168,224)(169,223)(170,222)(227,284)(228,283)(229,289)(230,288)(231,287)(232,286)(233,285)(234,291)(235,290)(236,296)(237,295)(238,294)(239,293)(240,292)(241,298)(242,297)(243,303)(244,302)(245,301)(246,300)(247,299)(248,305)(249,304)(250,310)(251,309)(252,308)(253,307)(254,306)(255,312)(256,311)(257,317)(258,316)(259,315)(260,314)(261,313)(262,319)(263,318)(264,324)(265,323)(266,322)(267,321)(268,320)(269,326)(270,325)(271,331)(272,330)(273,329)(274,328)(275,327)(276,333)(277,332)(278,338)(279,337)(280,336)(281,335)(282,334)(339,396)(340,395)(341,401)(342,400)(343,399)(344,398)(345,397)(346,403)(347,402)(348,408)(349,407)(350,406)(351,405)(352,404)(353,410)(354,409)(355,415)(356,414)(357,413)(358,412)(359,411)(360,417)(361,416)(362,422)(363,421)(364,420)(365,419)(366,418)(367,424)(368,423)(369,429)(370,428)(371,427)(372,426)(373,425)(374,431)(375,430)(376,436)(377,435)(378,434)(379,433)(380,432)(381,438)(382,437)(383,443)(384,442)(385,441)(386,440)(387,439)(388,445)(389,444)(390,450)(391,449)(392,448)(393,447)(394,446);
poly := sub<Sym(450)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;