Polytope of Type {18,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,12,3}*1728
if this polytope has a name.
Group : SmallGroup(1728,30201)
Rank : 4
Schlafli Type : {18,12,3}
Number of vertices, edges, etc : 18, 144, 24, 4
Order of s0s1s2s3 : 72
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {18,6,3}*864
3-fold quotients : {6,12,3}*576
6-fold quotients : {6,6,3}*288
9-fold quotients : {2,12,3}*192
18-fold quotients : {2,6,3}*96
36-fold quotients : {2,3,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)( 16, 24)
( 25, 65)( 26, 66)( 27, 67)( 28, 68)( 29, 69)( 30, 70)( 31, 71)( 32, 72)
( 33, 57)( 34, 58)( 35, 59)( 36, 60)( 37, 61)( 38, 62)( 39, 63)( 40, 64)
( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)( 48, 56)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
( 97,137)( 98,138)( 99,139)(100,140)(101,141)(102,142)(103,143)(104,144)
(105,129)(106,130)(107,131)(108,132)(109,133)(110,134)(111,135)(112,136)
(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)
(153,161)(154,162)(155,163)(156,164)(157,165)(158,166)(159,167)(160,168)
(169,209)(170,210)(171,211)(172,212)(173,213)(174,214)(175,215)(176,216)
(177,201)(178,202)(179,203)(180,204)(181,205)(182,206)(183,207)(184,208)
(185,193)(186,194)(187,195)(188,196)(189,197)(190,198)(191,199)(192,200)
(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)(232,240)
(241,281)(242,282)(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)
(249,273)(250,274)(251,275)(252,276)(253,277)(254,278)(255,279)(256,280)
(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)(264,272)
(297,305)(298,306)(299,307)(300,308)(301,309)(302,310)(303,311)(304,312)
(313,353)(314,354)(315,355)(316,356)(317,357)(318,358)(319,359)(320,360)
(321,345)(322,346)(323,347)(324,348)(325,349)(326,350)(327,351)(328,352)
(329,337)(330,338)(331,339)(332,340)(333,341)(334,342)(335,343)(336,344)
(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)(376,384)
(385,425)(386,426)(387,427)(388,428)(389,429)(390,430)(391,431)(392,432)
(393,417)(394,418)(395,419)(396,420)(397,421)(398,422)(399,423)(400,424)
(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)(408,416);;
s1 := ( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 31)( 6, 32)( 7, 29)( 8, 30)
( 9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)( 16, 46)
( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 39)( 22, 40)( 23, 37)( 24, 38)
( 49, 65)( 50, 66)( 51, 68)( 52, 67)( 53, 71)( 54, 72)( 55, 69)( 56, 70)
( 59, 60)( 61, 63)( 62, 64)( 73,169)( 74,170)( 75,172)( 76,171)( 77,175)
( 78,176)( 79,173)( 80,174)( 81,185)( 82,186)( 83,188)( 84,187)( 85,191)
( 86,192)( 87,189)( 88,190)( 89,177)( 90,178)( 91,180)( 92,179)( 93,183)
( 94,184)( 95,181)( 96,182)( 97,145)( 98,146)( 99,148)(100,147)(101,151)
(102,152)(103,149)(104,150)(105,161)(106,162)(107,164)(108,163)(109,167)
(110,168)(111,165)(112,166)(113,153)(114,154)(115,156)(116,155)(117,159)
(118,160)(119,157)(120,158)(121,209)(122,210)(123,212)(124,211)(125,215)
(126,216)(127,213)(128,214)(129,201)(130,202)(131,204)(132,203)(133,207)
(134,208)(135,205)(136,206)(137,193)(138,194)(139,196)(140,195)(141,199)
(142,200)(143,197)(144,198)(217,242)(218,241)(219,243)(220,244)(221,248)
(222,247)(223,246)(224,245)(225,258)(226,257)(227,259)(228,260)(229,264)
(230,263)(231,262)(232,261)(233,250)(234,249)(235,251)(236,252)(237,256)
(238,255)(239,254)(240,253)(265,282)(266,281)(267,283)(268,284)(269,288)
(270,287)(271,286)(272,285)(273,274)(277,280)(278,279)(289,386)(290,385)
(291,387)(292,388)(293,392)(294,391)(295,390)(296,389)(297,402)(298,401)
(299,403)(300,404)(301,408)(302,407)(303,406)(304,405)(305,394)(306,393)
(307,395)(308,396)(309,400)(310,399)(311,398)(312,397)(313,362)(314,361)
(315,363)(316,364)(317,368)(318,367)(319,366)(320,365)(321,378)(322,377)
(323,379)(324,380)(325,384)(326,383)(327,382)(328,381)(329,370)(330,369)
(331,371)(332,372)(333,376)(334,375)(335,374)(336,373)(337,426)(338,425)
(339,427)(340,428)(341,432)(342,431)(343,430)(344,429)(345,418)(346,417)
(347,419)(348,420)(349,424)(350,423)(351,422)(352,421)(353,410)(354,409)
(355,411)(356,412)(357,416)(358,415)(359,414)(360,413);;
s2 := ( 1,289)( 2,290)( 3,295)( 4,296)( 5,294)( 6,293)( 7,291)( 8,292)
( 9,297)( 10,298)( 11,303)( 12,304)( 13,302)( 14,301)( 15,299)( 16,300)
( 17,305)( 18,306)( 19,311)( 20,312)( 21,310)( 22,309)( 23,307)( 24,308)
( 25,313)( 26,314)( 27,319)( 28,320)( 29,318)( 30,317)( 31,315)( 32,316)
( 33,321)( 34,322)( 35,327)( 36,328)( 37,326)( 38,325)( 39,323)( 40,324)
( 41,329)( 42,330)( 43,335)( 44,336)( 45,334)( 46,333)( 47,331)( 48,332)
( 49,337)( 50,338)( 51,343)( 52,344)( 53,342)( 54,341)( 55,339)( 56,340)
( 57,345)( 58,346)( 59,351)( 60,352)( 61,350)( 62,349)( 63,347)( 64,348)
( 65,353)( 66,354)( 67,359)( 68,360)( 69,358)( 70,357)( 71,355)( 72,356)
( 73,217)( 74,218)( 75,223)( 76,224)( 77,222)( 78,221)( 79,219)( 80,220)
( 81,225)( 82,226)( 83,231)( 84,232)( 85,230)( 86,229)( 87,227)( 88,228)
( 89,233)( 90,234)( 91,239)( 92,240)( 93,238)( 94,237)( 95,235)( 96,236)
( 97,241)( 98,242)( 99,247)(100,248)(101,246)(102,245)(103,243)(104,244)
(105,249)(106,250)(107,255)(108,256)(109,254)(110,253)(111,251)(112,252)
(113,257)(114,258)(115,263)(116,264)(117,262)(118,261)(119,259)(120,260)
(121,265)(122,266)(123,271)(124,272)(125,270)(126,269)(127,267)(128,268)
(129,273)(130,274)(131,279)(132,280)(133,278)(134,277)(135,275)(136,276)
(137,281)(138,282)(139,287)(140,288)(141,286)(142,285)(143,283)(144,284)
(145,361)(146,362)(147,367)(148,368)(149,366)(150,365)(151,363)(152,364)
(153,369)(154,370)(155,375)(156,376)(157,374)(158,373)(159,371)(160,372)
(161,377)(162,378)(163,383)(164,384)(165,382)(166,381)(167,379)(168,380)
(169,385)(170,386)(171,391)(172,392)(173,390)(174,389)(175,387)(176,388)
(177,393)(178,394)(179,399)(180,400)(181,398)(182,397)(183,395)(184,396)
(185,401)(186,402)(187,407)(188,408)(189,406)(190,405)(191,403)(192,404)
(193,409)(194,410)(195,415)(196,416)(197,414)(198,413)(199,411)(200,412)
(201,417)(202,418)(203,423)(204,424)(205,422)(206,421)(207,419)(208,420)
(209,425)(210,426)(211,431)(212,432)(213,430)(214,429)(215,427)(216,428);;
s3 := ( 1,219)( 2,220)( 3,217)( 4,218)( 5,222)( 6,221)( 7,223)( 8,224)
( 9,227)( 10,228)( 11,225)( 12,226)( 13,230)( 14,229)( 15,231)( 16,232)
( 17,235)( 18,236)( 19,233)( 20,234)( 21,238)( 22,237)( 23,239)( 24,240)
( 25,243)( 26,244)( 27,241)( 28,242)( 29,246)( 30,245)( 31,247)( 32,248)
( 33,251)( 34,252)( 35,249)( 36,250)( 37,254)( 38,253)( 39,255)( 40,256)
( 41,259)( 42,260)( 43,257)( 44,258)( 45,262)( 46,261)( 47,263)( 48,264)
( 49,267)( 50,268)( 51,265)( 52,266)( 53,270)( 54,269)( 55,271)( 56,272)
( 57,275)( 58,276)( 59,273)( 60,274)( 61,278)( 62,277)( 63,279)( 64,280)
( 65,283)( 66,284)( 67,281)( 68,282)( 69,286)( 70,285)( 71,287)( 72,288)
( 73,363)( 74,364)( 75,361)( 76,362)( 77,366)( 78,365)( 79,367)( 80,368)
( 81,371)( 82,372)( 83,369)( 84,370)( 85,374)( 86,373)( 87,375)( 88,376)
( 89,379)( 90,380)( 91,377)( 92,378)( 93,382)( 94,381)( 95,383)( 96,384)
( 97,387)( 98,388)( 99,385)(100,386)(101,390)(102,389)(103,391)(104,392)
(105,395)(106,396)(107,393)(108,394)(109,398)(110,397)(111,399)(112,400)
(113,403)(114,404)(115,401)(116,402)(117,406)(118,405)(119,407)(120,408)
(121,411)(122,412)(123,409)(124,410)(125,414)(126,413)(127,415)(128,416)
(129,419)(130,420)(131,417)(132,418)(133,422)(134,421)(135,423)(136,424)
(137,427)(138,428)(139,425)(140,426)(141,430)(142,429)(143,431)(144,432)
(145,291)(146,292)(147,289)(148,290)(149,294)(150,293)(151,295)(152,296)
(153,299)(154,300)(155,297)(156,298)(157,302)(158,301)(159,303)(160,304)
(161,307)(162,308)(163,305)(164,306)(165,310)(166,309)(167,311)(168,312)
(169,315)(170,316)(171,313)(172,314)(173,318)(174,317)(175,319)(176,320)
(177,323)(178,324)(179,321)(180,322)(181,326)(182,325)(183,327)(184,328)
(185,331)(186,332)(187,329)(188,330)(189,334)(190,333)(191,335)(192,336)
(193,339)(194,340)(195,337)(196,338)(197,342)(198,341)(199,343)(200,344)
(201,347)(202,348)(203,345)(204,346)(205,350)(206,349)(207,351)(208,352)
(209,355)(210,356)(211,353)(212,354)(213,358)(214,357)(215,359)(216,360);;
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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s1*s2*s3*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*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 13, 21)( 14, 22)( 15, 23)
( 16, 24)( 25, 65)( 26, 66)( 27, 67)( 28, 68)( 29, 69)( 30, 70)( 31, 71)
( 32, 72)( 33, 57)( 34, 58)( 35, 59)( 36, 60)( 37, 61)( 38, 62)( 39, 63)
( 40, 64)( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)
( 48, 56)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)( 97,137)( 98,138)( 99,139)(100,140)(101,141)(102,142)(103,143)
(104,144)(105,129)(106,130)(107,131)(108,132)(109,133)(110,134)(111,135)
(112,136)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)
(120,128)(153,161)(154,162)(155,163)(156,164)(157,165)(158,166)(159,167)
(160,168)(169,209)(170,210)(171,211)(172,212)(173,213)(174,214)(175,215)
(176,216)(177,201)(178,202)(179,203)(180,204)(181,205)(182,206)(183,207)
(184,208)(185,193)(186,194)(187,195)(188,196)(189,197)(190,198)(191,199)
(192,200)(225,233)(226,234)(227,235)(228,236)(229,237)(230,238)(231,239)
(232,240)(241,281)(242,282)(243,283)(244,284)(245,285)(246,286)(247,287)
(248,288)(249,273)(250,274)(251,275)(252,276)(253,277)(254,278)(255,279)
(256,280)(257,265)(258,266)(259,267)(260,268)(261,269)(262,270)(263,271)
(264,272)(297,305)(298,306)(299,307)(300,308)(301,309)(302,310)(303,311)
(304,312)(313,353)(314,354)(315,355)(316,356)(317,357)(318,358)(319,359)
(320,360)(321,345)(322,346)(323,347)(324,348)(325,349)(326,350)(327,351)
(328,352)(329,337)(330,338)(331,339)(332,340)(333,341)(334,342)(335,343)
(336,344)(369,377)(370,378)(371,379)(372,380)(373,381)(374,382)(375,383)
(376,384)(385,425)(386,426)(387,427)(388,428)(389,429)(390,430)(391,431)
(392,432)(393,417)(394,418)(395,419)(396,420)(397,421)(398,422)(399,423)
(400,424)(401,409)(402,410)(403,411)(404,412)(405,413)(406,414)(407,415)
(408,416);
s1 := Sym(432)!( 1, 25)( 2, 26)( 3, 28)( 4, 27)( 5, 31)( 6, 32)( 7, 29)
( 8, 30)( 9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)
( 16, 46)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 39)( 22, 40)( 23, 37)
( 24, 38)( 49, 65)( 50, 66)( 51, 68)( 52, 67)( 53, 71)( 54, 72)( 55, 69)
( 56, 70)( 59, 60)( 61, 63)( 62, 64)( 73,169)( 74,170)( 75,172)( 76,171)
( 77,175)( 78,176)( 79,173)( 80,174)( 81,185)( 82,186)( 83,188)( 84,187)
( 85,191)( 86,192)( 87,189)( 88,190)( 89,177)( 90,178)( 91,180)( 92,179)
( 93,183)( 94,184)( 95,181)( 96,182)( 97,145)( 98,146)( 99,148)(100,147)
(101,151)(102,152)(103,149)(104,150)(105,161)(106,162)(107,164)(108,163)
(109,167)(110,168)(111,165)(112,166)(113,153)(114,154)(115,156)(116,155)
(117,159)(118,160)(119,157)(120,158)(121,209)(122,210)(123,212)(124,211)
(125,215)(126,216)(127,213)(128,214)(129,201)(130,202)(131,204)(132,203)
(133,207)(134,208)(135,205)(136,206)(137,193)(138,194)(139,196)(140,195)
(141,199)(142,200)(143,197)(144,198)(217,242)(218,241)(219,243)(220,244)
(221,248)(222,247)(223,246)(224,245)(225,258)(226,257)(227,259)(228,260)
(229,264)(230,263)(231,262)(232,261)(233,250)(234,249)(235,251)(236,252)
(237,256)(238,255)(239,254)(240,253)(265,282)(266,281)(267,283)(268,284)
(269,288)(270,287)(271,286)(272,285)(273,274)(277,280)(278,279)(289,386)
(290,385)(291,387)(292,388)(293,392)(294,391)(295,390)(296,389)(297,402)
(298,401)(299,403)(300,404)(301,408)(302,407)(303,406)(304,405)(305,394)
(306,393)(307,395)(308,396)(309,400)(310,399)(311,398)(312,397)(313,362)
(314,361)(315,363)(316,364)(317,368)(318,367)(319,366)(320,365)(321,378)
(322,377)(323,379)(324,380)(325,384)(326,383)(327,382)(328,381)(329,370)
(330,369)(331,371)(332,372)(333,376)(334,375)(335,374)(336,373)(337,426)
(338,425)(339,427)(340,428)(341,432)(342,431)(343,430)(344,429)(345,418)
(346,417)(347,419)(348,420)(349,424)(350,423)(351,422)(352,421)(353,410)
(354,409)(355,411)(356,412)(357,416)(358,415)(359,414)(360,413);
s2 := Sym(432)!( 1,289)( 2,290)( 3,295)( 4,296)( 5,294)( 6,293)( 7,291)
( 8,292)( 9,297)( 10,298)( 11,303)( 12,304)( 13,302)( 14,301)( 15,299)
( 16,300)( 17,305)( 18,306)( 19,311)( 20,312)( 21,310)( 22,309)( 23,307)
( 24,308)( 25,313)( 26,314)( 27,319)( 28,320)( 29,318)( 30,317)( 31,315)
( 32,316)( 33,321)( 34,322)( 35,327)( 36,328)( 37,326)( 38,325)( 39,323)
( 40,324)( 41,329)( 42,330)( 43,335)( 44,336)( 45,334)( 46,333)( 47,331)
( 48,332)( 49,337)( 50,338)( 51,343)( 52,344)( 53,342)( 54,341)( 55,339)
( 56,340)( 57,345)( 58,346)( 59,351)( 60,352)( 61,350)( 62,349)( 63,347)
( 64,348)( 65,353)( 66,354)( 67,359)( 68,360)( 69,358)( 70,357)( 71,355)
( 72,356)( 73,217)( 74,218)( 75,223)( 76,224)( 77,222)( 78,221)( 79,219)
( 80,220)( 81,225)( 82,226)( 83,231)( 84,232)( 85,230)( 86,229)( 87,227)
( 88,228)( 89,233)( 90,234)( 91,239)( 92,240)( 93,238)( 94,237)( 95,235)
( 96,236)( 97,241)( 98,242)( 99,247)(100,248)(101,246)(102,245)(103,243)
(104,244)(105,249)(106,250)(107,255)(108,256)(109,254)(110,253)(111,251)
(112,252)(113,257)(114,258)(115,263)(116,264)(117,262)(118,261)(119,259)
(120,260)(121,265)(122,266)(123,271)(124,272)(125,270)(126,269)(127,267)
(128,268)(129,273)(130,274)(131,279)(132,280)(133,278)(134,277)(135,275)
(136,276)(137,281)(138,282)(139,287)(140,288)(141,286)(142,285)(143,283)
(144,284)(145,361)(146,362)(147,367)(148,368)(149,366)(150,365)(151,363)
(152,364)(153,369)(154,370)(155,375)(156,376)(157,374)(158,373)(159,371)
(160,372)(161,377)(162,378)(163,383)(164,384)(165,382)(166,381)(167,379)
(168,380)(169,385)(170,386)(171,391)(172,392)(173,390)(174,389)(175,387)
(176,388)(177,393)(178,394)(179,399)(180,400)(181,398)(182,397)(183,395)
(184,396)(185,401)(186,402)(187,407)(188,408)(189,406)(190,405)(191,403)
(192,404)(193,409)(194,410)(195,415)(196,416)(197,414)(198,413)(199,411)
(200,412)(201,417)(202,418)(203,423)(204,424)(205,422)(206,421)(207,419)
(208,420)(209,425)(210,426)(211,431)(212,432)(213,430)(214,429)(215,427)
(216,428);
s3 := Sym(432)!( 1,219)( 2,220)( 3,217)( 4,218)( 5,222)( 6,221)( 7,223)
( 8,224)( 9,227)( 10,228)( 11,225)( 12,226)( 13,230)( 14,229)( 15,231)
( 16,232)( 17,235)( 18,236)( 19,233)( 20,234)( 21,238)( 22,237)( 23,239)
( 24,240)( 25,243)( 26,244)( 27,241)( 28,242)( 29,246)( 30,245)( 31,247)
( 32,248)( 33,251)( 34,252)( 35,249)( 36,250)( 37,254)( 38,253)( 39,255)
( 40,256)( 41,259)( 42,260)( 43,257)( 44,258)( 45,262)( 46,261)( 47,263)
( 48,264)( 49,267)( 50,268)( 51,265)( 52,266)( 53,270)( 54,269)( 55,271)
( 56,272)( 57,275)( 58,276)( 59,273)( 60,274)( 61,278)( 62,277)( 63,279)
( 64,280)( 65,283)( 66,284)( 67,281)( 68,282)( 69,286)( 70,285)( 71,287)
( 72,288)( 73,363)( 74,364)( 75,361)( 76,362)( 77,366)( 78,365)( 79,367)
( 80,368)( 81,371)( 82,372)( 83,369)( 84,370)( 85,374)( 86,373)( 87,375)
( 88,376)( 89,379)( 90,380)( 91,377)( 92,378)( 93,382)( 94,381)( 95,383)
( 96,384)( 97,387)( 98,388)( 99,385)(100,386)(101,390)(102,389)(103,391)
(104,392)(105,395)(106,396)(107,393)(108,394)(109,398)(110,397)(111,399)
(112,400)(113,403)(114,404)(115,401)(116,402)(117,406)(118,405)(119,407)
(120,408)(121,411)(122,412)(123,409)(124,410)(125,414)(126,413)(127,415)
(128,416)(129,419)(130,420)(131,417)(132,418)(133,422)(134,421)(135,423)
(136,424)(137,427)(138,428)(139,425)(140,426)(141,430)(142,429)(143,431)
(144,432)(145,291)(146,292)(147,289)(148,290)(149,294)(150,293)(151,295)
(152,296)(153,299)(154,300)(155,297)(156,298)(157,302)(158,301)(159,303)
(160,304)(161,307)(162,308)(163,305)(164,306)(165,310)(166,309)(167,311)
(168,312)(169,315)(170,316)(171,313)(172,314)(173,318)(174,317)(175,319)
(176,320)(177,323)(178,324)(179,321)(180,322)(181,326)(182,325)(183,327)
(184,328)(185,331)(186,332)(187,329)(188,330)(189,334)(190,333)(191,335)
(192,336)(193,339)(194,340)(195,337)(196,338)(197,342)(198,341)(199,343)
(200,344)(201,347)(202,348)(203,345)(204,346)(205,350)(206,349)(207,351)
(208,352)(209,355)(210,356)(211,353)(212,354)(213,358)(214,357)(215,359)
(216,360);
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,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s1*s2*s3*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*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope