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