Polytope of Type {3,24,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,24,6}*1728a
if this polytope has a name.
Group : SmallGroup(1728,30298)
Rank : 4
Schlafli Type : {3,24,6}
Number of vertices, edges, etc : 6, 72, 144, 6
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 6
Special Properties :
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 : {3,12,6}*864a
3-fold quotients : {3,8,6}*576
6-fold quotients : {3,4,6}*288
8-fold quotients : {3,6,6}*216a
9-fold quotients : {3,8,2}*192
16-fold quotients : {3,6,3}*108
18-fold quotients : {3,4,2}*96
24-fold quotients : {3,2,6}*72
36-fold quotients : {3,4,2}*48
48-fold quotients : {3,2,3}*36
72-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 13, 23)
( 14, 24)( 15, 21)( 16, 22)( 27, 28)( 29, 31)( 30, 32)( 33, 41)( 34, 42)
( 35, 44)( 36, 43)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 51, 52)( 53, 55)
( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)( 63, 69)
( 64, 70)( 73,145)( 74,146)( 75,148)( 76,147)( 77,151)( 78,152)( 79,149)
( 80,150)( 81,161)( 82,162)( 83,164)( 84,163)( 85,167)( 86,168)( 87,165)
( 88,166)( 89,153)( 90,154)( 91,156)( 92,155)( 93,159)( 94,160)( 95,157)
( 96,158)( 97,169)( 98,170)( 99,172)(100,171)(101,175)(102,176)(103,173)
(104,174)(105,185)(106,186)(107,188)(108,187)(109,191)(110,192)(111,189)
(112,190)(113,177)(114,178)(115,180)(116,179)(117,183)(118,184)(119,181)
(120,182)(121,193)(122,194)(123,196)(124,195)(125,199)(126,200)(127,197)
(128,198)(129,209)(130,210)(131,212)(132,211)(133,215)(134,216)(135,213)
(136,214)(137,201)(138,202)(139,204)(140,203)(141,207)(142,208)(143,205)
(144,206)(217,218)(221,224)(222,223)(225,234)(226,233)(227,235)(228,236)
(229,240)(230,239)(231,238)(232,237)(241,242)(245,248)(246,247)(249,258)
(250,257)(251,259)(252,260)(253,264)(254,263)(255,262)(256,261)(265,266)
(269,272)(270,271)(273,282)(274,281)(275,283)(276,284)(277,288)(278,287)
(279,286)(280,285)(289,362)(290,361)(291,363)(292,364)(293,368)(294,367)
(295,366)(296,365)(297,378)(298,377)(299,379)(300,380)(301,384)(302,383)
(303,382)(304,381)(305,370)(306,369)(307,371)(308,372)(309,376)(310,375)
(311,374)(312,373)(313,386)(314,385)(315,387)(316,388)(317,392)(318,391)
(319,390)(320,389)(321,402)(322,401)(323,403)(324,404)(325,408)(326,407)
(327,406)(328,405)(329,394)(330,393)(331,395)(332,396)(333,400)(334,399)
(335,398)(336,397)(337,410)(338,409)(339,411)(340,412)(341,416)(342,415)
(343,414)(344,413)(345,426)(346,425)(347,427)(348,428)(349,432)(350,431)
(351,430)(352,429)(353,418)(354,417)(355,419)(356,420)(357,424)(358,423)
(359,422)(360,421);;
s1 := ( 1, 73)( 2, 74)( 3, 79)( 4, 80)( 5, 78)( 6, 77)( 7, 75)( 8, 76)
( 9, 89)( 10, 90)( 11, 95)( 12, 96)( 13, 94)( 14, 93)( 15, 91)( 16, 92)
( 17, 81)( 18, 82)( 19, 87)( 20, 88)( 21, 86)( 22, 85)( 23, 83)( 24, 84)
( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)( 32,108)
( 33, 97)( 34, 98)( 35,103)( 36,104)( 37,102)( 38,101)( 39, 99)( 40,100)
( 41,113)( 42,114)( 43,119)( 44,120)( 45,118)( 46,117)( 47,115)( 48,116)
( 49,137)( 50,138)( 51,143)( 52,144)( 53,142)( 54,141)( 55,139)( 56,140)
( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)( 64,132)
( 65,121)( 66,122)( 67,127)( 68,128)( 69,126)( 70,125)( 71,123)( 72,124)
(147,151)(148,152)(149,150)(153,161)(154,162)(155,167)(156,168)(157,166)
(158,165)(159,163)(160,164)(169,177)(170,178)(171,183)(172,184)(173,182)
(174,181)(175,179)(176,180)(187,191)(188,192)(189,190)(193,209)(194,210)
(195,215)(196,216)(197,214)(198,213)(199,211)(200,212)(203,207)(204,208)
(205,206)(217,290)(218,289)(219,296)(220,295)(221,293)(222,294)(223,292)
(224,291)(225,306)(226,305)(227,312)(228,311)(229,309)(230,310)(231,308)
(232,307)(233,298)(234,297)(235,304)(236,303)(237,301)(238,302)(239,300)
(240,299)(241,322)(242,321)(243,328)(244,327)(245,325)(246,326)(247,324)
(248,323)(249,314)(250,313)(251,320)(252,319)(253,317)(254,318)(255,316)
(256,315)(257,330)(258,329)(259,336)(260,335)(261,333)(262,334)(263,332)
(264,331)(265,354)(266,353)(267,360)(268,359)(269,357)(270,358)(271,356)
(272,355)(273,346)(274,345)(275,352)(276,351)(277,349)(278,350)(279,348)
(280,347)(281,338)(282,337)(283,344)(284,343)(285,341)(286,342)(287,340)
(288,339)(361,362)(363,368)(364,367)(369,378)(370,377)(371,384)(372,383)
(373,381)(374,382)(375,380)(376,379)(385,394)(386,393)(387,400)(388,399)
(389,397)(390,398)(391,396)(392,395)(401,402)(403,408)(404,407)(409,426)
(410,425)(411,432)(412,431)(413,429)(414,430)(415,428)(416,427)(417,418)
(419,424)(420,423);;
s2 := ( 1,243)( 2,244)( 3,242)( 4,241)( 5,247)( 6,248)( 7,246)( 8,245)
( 9,259)( 10,260)( 11,258)( 12,257)( 13,263)( 14,264)( 15,262)( 16,261)
( 17,251)( 18,252)( 19,250)( 20,249)( 21,255)( 22,256)( 23,254)( 24,253)
( 25,219)( 26,220)( 27,218)( 28,217)( 29,223)( 30,224)( 31,222)( 32,221)
( 33,235)( 34,236)( 35,234)( 36,233)( 37,239)( 38,240)( 39,238)( 40,237)
( 41,227)( 42,228)( 43,226)( 44,225)( 45,231)( 46,232)( 47,230)( 48,229)
( 49,267)( 50,268)( 51,266)( 52,265)( 53,271)( 54,272)( 55,270)( 56,269)
( 57,283)( 58,284)( 59,282)( 60,281)( 61,287)( 62,288)( 63,286)( 64,285)
( 65,275)( 66,276)( 67,274)( 68,273)( 69,279)( 70,280)( 71,278)( 72,277)
( 73,315)( 74,316)( 75,314)( 76,313)( 77,319)( 78,320)( 79,318)( 80,317)
( 81,331)( 82,332)( 83,330)( 84,329)( 85,335)( 86,336)( 87,334)( 88,333)
( 89,323)( 90,324)( 91,322)( 92,321)( 93,327)( 94,328)( 95,326)( 96,325)
( 97,291)( 98,292)( 99,290)(100,289)(101,295)(102,296)(103,294)(104,293)
(105,307)(106,308)(107,306)(108,305)(109,311)(110,312)(111,310)(112,309)
(113,299)(114,300)(115,298)(116,297)(117,303)(118,304)(119,302)(120,301)
(121,339)(122,340)(123,338)(124,337)(125,343)(126,344)(127,342)(128,341)
(129,355)(130,356)(131,354)(132,353)(133,359)(134,360)(135,358)(136,357)
(137,347)(138,348)(139,346)(140,345)(141,351)(142,352)(143,350)(144,349)
(145,387)(146,388)(147,386)(148,385)(149,391)(150,392)(151,390)(152,389)
(153,403)(154,404)(155,402)(156,401)(157,407)(158,408)(159,406)(160,405)
(161,395)(162,396)(163,394)(164,393)(165,399)(166,400)(167,398)(168,397)
(169,363)(170,364)(171,362)(172,361)(173,367)(174,368)(175,366)(176,365)
(177,379)(178,380)(179,378)(180,377)(181,383)(182,384)(183,382)(184,381)
(185,371)(186,372)(187,370)(188,369)(189,375)(190,376)(191,374)(192,373)
(193,411)(194,412)(195,410)(196,409)(197,415)(198,416)(199,414)(200,413)
(201,427)(202,428)(203,426)(204,425)(205,431)(206,432)(207,430)(208,429)
(209,419)(210,420)(211,418)(212,417)(213,423)(214,424)(215,422)(216,421);;
s3 := ( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)
( 25, 49)( 26, 50)( 27, 51)( 28, 52)( 29, 53)( 30, 54)( 31, 55)( 32, 56)
( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 69)( 38, 70)( 39, 71)( 40, 72)
( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)( 48, 64)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)(103,127)(104,128)
(105,137)(106,138)(107,139)(108,140)(109,141)(110,142)(111,143)(112,144)
(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)(120,136)
(153,161)(154,162)(155,163)(156,164)(157,165)(158,166)(159,167)(160,168)
(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)(176,200)
(177,209)(178,210)(179,211)(180,212)(181,213)(182,214)(183,215)(184,216)
(185,201)(186,202)(187,203)(188,204)(189,205)(190,206)(191,207)(192,208)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)(248,272)
(249,281)(250,282)(251,283)(252,284)(253,285)(254,286)(255,287)(256,288)
(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)(264,280)
(297,305)(298,306)(299,307)(300,308)(301,309)(302,310)(303,311)(304,312)
(313,337)(314,338)(315,339)(316,340)(317,341)(318,342)(319,343)(320,344)
(321,353)(322,354)(323,355)(324,356)(325,357)(326,358)(327,359)(328,360)
(329,345)(330,346)(331,347)(332,348)(333,349)(334,350)(335,351)(336,352)
(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)
(385,409)(386,410)(387,411)(388,412)(389,413)(390,414)(391,415)(392,416)
(393,425)(394,426)(395,427)(396,428)(397,429)(398,430)(399,431)(400,432)
(401,417)(402,418)(403,419)(404,420)(405,421)(406,422)(407,423)(408,424);;
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, s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s2*s0*s1*s2*s1*s0*s3*s2*s1*s2*s3*s0*s1*s2*s1*s2*s0*s1,
s3*s0*s2*s3*s2*s1*s3*s2*s3*s2*s0*s1*s3*s2*s3*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 3, 4)( 5, 7)( 6, 8)( 9, 17)( 10, 18)( 11, 20)( 12, 19)
( 13, 23)( 14, 24)( 15, 21)( 16, 22)( 27, 28)( 29, 31)( 30, 32)( 33, 41)
( 34, 42)( 35, 44)( 36, 43)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 51, 52)
( 53, 55)( 54, 56)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 61, 71)( 62, 72)
( 63, 69)( 64, 70)( 73,145)( 74,146)( 75,148)( 76,147)( 77,151)( 78,152)
( 79,149)( 80,150)( 81,161)( 82,162)( 83,164)( 84,163)( 85,167)( 86,168)
( 87,165)( 88,166)( 89,153)( 90,154)( 91,156)( 92,155)( 93,159)( 94,160)
( 95,157)( 96,158)( 97,169)( 98,170)( 99,172)(100,171)(101,175)(102,176)
(103,173)(104,174)(105,185)(106,186)(107,188)(108,187)(109,191)(110,192)
(111,189)(112,190)(113,177)(114,178)(115,180)(116,179)(117,183)(118,184)
(119,181)(120,182)(121,193)(122,194)(123,196)(124,195)(125,199)(126,200)
(127,197)(128,198)(129,209)(130,210)(131,212)(132,211)(133,215)(134,216)
(135,213)(136,214)(137,201)(138,202)(139,204)(140,203)(141,207)(142,208)
(143,205)(144,206)(217,218)(221,224)(222,223)(225,234)(226,233)(227,235)
(228,236)(229,240)(230,239)(231,238)(232,237)(241,242)(245,248)(246,247)
(249,258)(250,257)(251,259)(252,260)(253,264)(254,263)(255,262)(256,261)
(265,266)(269,272)(270,271)(273,282)(274,281)(275,283)(276,284)(277,288)
(278,287)(279,286)(280,285)(289,362)(290,361)(291,363)(292,364)(293,368)
(294,367)(295,366)(296,365)(297,378)(298,377)(299,379)(300,380)(301,384)
(302,383)(303,382)(304,381)(305,370)(306,369)(307,371)(308,372)(309,376)
(310,375)(311,374)(312,373)(313,386)(314,385)(315,387)(316,388)(317,392)
(318,391)(319,390)(320,389)(321,402)(322,401)(323,403)(324,404)(325,408)
(326,407)(327,406)(328,405)(329,394)(330,393)(331,395)(332,396)(333,400)
(334,399)(335,398)(336,397)(337,410)(338,409)(339,411)(340,412)(341,416)
(342,415)(343,414)(344,413)(345,426)(346,425)(347,427)(348,428)(349,432)
(350,431)(351,430)(352,429)(353,418)(354,417)(355,419)(356,420)(357,424)
(358,423)(359,422)(360,421);
s1 := Sym(432)!( 1, 73)( 2, 74)( 3, 79)( 4, 80)( 5, 78)( 6, 77)( 7, 75)
( 8, 76)( 9, 89)( 10, 90)( 11, 95)( 12, 96)( 13, 94)( 14, 93)( 15, 91)
( 16, 92)( 17, 81)( 18, 82)( 19, 87)( 20, 88)( 21, 86)( 22, 85)( 23, 83)
( 24, 84)( 25,105)( 26,106)( 27,111)( 28,112)( 29,110)( 30,109)( 31,107)
( 32,108)( 33, 97)( 34, 98)( 35,103)( 36,104)( 37,102)( 38,101)( 39, 99)
( 40,100)( 41,113)( 42,114)( 43,119)( 44,120)( 45,118)( 46,117)( 47,115)
( 48,116)( 49,137)( 50,138)( 51,143)( 52,144)( 53,142)( 54,141)( 55,139)
( 56,140)( 57,129)( 58,130)( 59,135)( 60,136)( 61,134)( 62,133)( 63,131)
( 64,132)( 65,121)( 66,122)( 67,127)( 68,128)( 69,126)( 70,125)( 71,123)
( 72,124)(147,151)(148,152)(149,150)(153,161)(154,162)(155,167)(156,168)
(157,166)(158,165)(159,163)(160,164)(169,177)(170,178)(171,183)(172,184)
(173,182)(174,181)(175,179)(176,180)(187,191)(188,192)(189,190)(193,209)
(194,210)(195,215)(196,216)(197,214)(198,213)(199,211)(200,212)(203,207)
(204,208)(205,206)(217,290)(218,289)(219,296)(220,295)(221,293)(222,294)
(223,292)(224,291)(225,306)(226,305)(227,312)(228,311)(229,309)(230,310)
(231,308)(232,307)(233,298)(234,297)(235,304)(236,303)(237,301)(238,302)
(239,300)(240,299)(241,322)(242,321)(243,328)(244,327)(245,325)(246,326)
(247,324)(248,323)(249,314)(250,313)(251,320)(252,319)(253,317)(254,318)
(255,316)(256,315)(257,330)(258,329)(259,336)(260,335)(261,333)(262,334)
(263,332)(264,331)(265,354)(266,353)(267,360)(268,359)(269,357)(270,358)
(271,356)(272,355)(273,346)(274,345)(275,352)(276,351)(277,349)(278,350)
(279,348)(280,347)(281,338)(282,337)(283,344)(284,343)(285,341)(286,342)
(287,340)(288,339)(361,362)(363,368)(364,367)(369,378)(370,377)(371,384)
(372,383)(373,381)(374,382)(375,380)(376,379)(385,394)(386,393)(387,400)
(388,399)(389,397)(390,398)(391,396)(392,395)(401,402)(403,408)(404,407)
(409,426)(410,425)(411,432)(412,431)(413,429)(414,430)(415,428)(416,427)
(417,418)(419,424)(420,423);
s2 := Sym(432)!( 1,243)( 2,244)( 3,242)( 4,241)( 5,247)( 6,248)( 7,246)
( 8,245)( 9,259)( 10,260)( 11,258)( 12,257)( 13,263)( 14,264)( 15,262)
( 16,261)( 17,251)( 18,252)( 19,250)( 20,249)( 21,255)( 22,256)( 23,254)
( 24,253)( 25,219)( 26,220)( 27,218)( 28,217)( 29,223)( 30,224)( 31,222)
( 32,221)( 33,235)( 34,236)( 35,234)( 36,233)( 37,239)( 38,240)( 39,238)
( 40,237)( 41,227)( 42,228)( 43,226)( 44,225)( 45,231)( 46,232)( 47,230)
( 48,229)( 49,267)( 50,268)( 51,266)( 52,265)( 53,271)( 54,272)( 55,270)
( 56,269)( 57,283)( 58,284)( 59,282)( 60,281)( 61,287)( 62,288)( 63,286)
( 64,285)( 65,275)( 66,276)( 67,274)( 68,273)( 69,279)( 70,280)( 71,278)
( 72,277)( 73,315)( 74,316)( 75,314)( 76,313)( 77,319)( 78,320)( 79,318)
( 80,317)( 81,331)( 82,332)( 83,330)( 84,329)( 85,335)( 86,336)( 87,334)
( 88,333)( 89,323)( 90,324)( 91,322)( 92,321)( 93,327)( 94,328)( 95,326)
( 96,325)( 97,291)( 98,292)( 99,290)(100,289)(101,295)(102,296)(103,294)
(104,293)(105,307)(106,308)(107,306)(108,305)(109,311)(110,312)(111,310)
(112,309)(113,299)(114,300)(115,298)(116,297)(117,303)(118,304)(119,302)
(120,301)(121,339)(122,340)(123,338)(124,337)(125,343)(126,344)(127,342)
(128,341)(129,355)(130,356)(131,354)(132,353)(133,359)(134,360)(135,358)
(136,357)(137,347)(138,348)(139,346)(140,345)(141,351)(142,352)(143,350)
(144,349)(145,387)(146,388)(147,386)(148,385)(149,391)(150,392)(151,390)
(152,389)(153,403)(154,404)(155,402)(156,401)(157,407)(158,408)(159,406)
(160,405)(161,395)(162,396)(163,394)(164,393)(165,399)(166,400)(167,398)
(168,397)(169,363)(170,364)(171,362)(172,361)(173,367)(174,368)(175,366)
(176,365)(177,379)(178,380)(179,378)(180,377)(181,383)(182,384)(183,382)
(184,381)(185,371)(186,372)(187,370)(188,369)(189,375)(190,376)(191,374)
(192,373)(193,411)(194,412)(195,410)(196,409)(197,415)(198,416)(199,414)
(200,413)(201,427)(202,428)(203,426)(204,425)(205,431)(206,432)(207,430)
(208,429)(209,419)(210,420)(211,418)(212,417)(213,423)(214,424)(215,422)
(216,421);
s3 := Sym(432)!( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)
( 16, 24)( 25, 49)( 26, 50)( 27, 51)( 28, 52)( 29, 53)( 30, 54)( 31, 55)
( 32, 56)( 33, 65)( 34, 66)( 35, 67)( 36, 68)( 37, 69)( 38, 70)( 39, 71)
( 40, 72)( 41, 57)( 42, 58)( 43, 59)( 44, 60)( 45, 61)( 46, 62)( 47, 63)
( 48, 64)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,121)( 98,122)( 99,123)(100,124)(101,125)(102,126)(103,127)
(104,128)(105,137)(106,138)(107,139)(108,140)(109,141)(110,142)(111,143)
(112,144)(113,129)(114,130)(115,131)(116,132)(117,133)(118,134)(119,135)
(120,136)(153,161)(154,162)(155,163)(156,164)(157,165)(158,166)(159,167)
(160,168)(169,193)(170,194)(171,195)(172,196)(173,197)(174,198)(175,199)
(176,200)(177,209)(178,210)(179,211)(180,212)(181,213)(182,214)(183,215)
(184,216)(185,201)(186,202)(187,203)(188,204)(189,205)(190,206)(191,207)
(192,208)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)
(248,272)(249,281)(250,282)(251,283)(252,284)(253,285)(254,286)(255,287)
(256,288)(257,273)(258,274)(259,275)(260,276)(261,277)(262,278)(263,279)
(264,280)(297,305)(298,306)(299,307)(300,308)(301,309)(302,310)(303,311)
(304,312)(313,337)(314,338)(315,339)(316,340)(317,341)(318,342)(319,343)
(320,344)(321,353)(322,354)(323,355)(324,356)(325,357)(326,358)(327,359)
(328,360)(329,345)(330,346)(331,347)(332,348)(333,349)(334,350)(335,351)
(336,352)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)
(376,384)(385,409)(386,410)(387,411)(388,412)(389,413)(390,414)(391,415)
(392,416)(393,425)(394,426)(395,427)(396,428)(397,429)(398,430)(399,431)
(400,432)(401,417)(402,418)(403,419)(404,420)(405,421)(406,422)(407,423)
(408,424);
poly := sub<Sym(432)|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,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s2*s0*s1*s2*s1*s0*s3*s2*s1*s2*s3*s0*s1*s2*s1*s2*s0*s1,
s3*s0*s2*s3*s2*s1*s3*s2*s3*s2*s0*s1*s3*s2*s3*s2*s0*s1 >;
References : None.
to this polytope