Polytope of Type {4,18,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,18,12}*1728d
if this polytope has a name.
Group : SmallGroup(1728,30313)
Rank : 4
Schlafli Type : {4,18,12}
Number of vertices, edges, etc : 4, 36, 108, 12
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-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 : {4,18,6}*864d
3-fold quotients : {4,18,4}*576c, {4,6,12}*576e
4-fold quotients : {4,9,6}*432
6-fold quotients : {4,18,2}*288b, {4,6,6}*288e
9-fold quotients : {4,6,4}*192c
12-fold quotients : {4,9,2}*144, {4,3,6}*144
18-fold quotients : {4,6,2}*96c
36-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)
(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)
(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432);;
s1 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 25)( 14, 26)( 15, 28)
( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)( 23, 32)
( 24, 31)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)
( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49,105)( 50,106)( 51,108)
( 52,107)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 97)( 58, 98)( 59,100)
( 60, 99)( 61, 93)( 62, 94)( 63, 96)( 64, 95)( 65, 89)( 66, 90)( 67, 92)
( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)(111,112)(113,117)(114,118)
(115,120)(116,119)(121,133)(122,134)(123,136)(124,135)(125,141)(126,142)
(127,144)(128,143)(129,137)(130,138)(131,140)(132,139)(145,189)(146,190)
(147,192)(148,191)(149,185)(150,186)(151,188)(152,187)(153,181)(154,182)
(155,184)(156,183)(157,213)(158,214)(159,216)(160,215)(161,209)(162,210)
(163,212)(164,211)(165,205)(166,206)(167,208)(168,207)(169,201)(170,202)
(171,204)(172,203)(173,197)(174,198)(175,200)(176,199)(177,193)(178,194)
(179,196)(180,195)(219,220)(221,225)(222,226)(223,228)(224,227)(229,241)
(230,242)(231,244)(232,243)(233,249)(234,250)(235,252)(236,251)(237,245)
(238,246)(239,248)(240,247)(253,297)(254,298)(255,300)(256,299)(257,293)
(258,294)(259,296)(260,295)(261,289)(262,290)(263,292)(264,291)(265,321)
(266,322)(267,324)(268,323)(269,317)(270,318)(271,320)(272,319)(273,313)
(274,314)(275,316)(276,315)(277,309)(278,310)(279,312)(280,311)(281,305)
(282,306)(283,308)(284,307)(285,301)(286,302)(287,304)(288,303)(327,328)
(329,333)(330,334)(331,336)(332,335)(337,349)(338,350)(339,352)(340,351)
(341,357)(342,358)(343,360)(344,359)(345,353)(346,354)(347,356)(348,355)
(361,405)(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)(368,403)
(369,397)(370,398)(371,400)(372,399)(373,429)(374,430)(375,432)(376,431)
(377,425)(378,426)(379,428)(380,427)(381,421)(382,422)(383,424)(384,423)
(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)(392,415)
(393,409)(394,410)(395,412)(396,411);;
s2 := ( 1,265)( 2,268)( 3,267)( 4,266)( 5,273)( 6,276)( 7,275)( 8,274)
( 9,269)( 10,272)( 11,271)( 12,270)( 13,253)( 14,256)( 15,255)( 16,254)
( 17,261)( 18,264)( 19,263)( 20,262)( 21,257)( 22,260)( 23,259)( 24,258)
( 25,277)( 26,280)( 27,279)( 28,278)( 29,285)( 30,288)( 31,287)( 32,286)
( 33,281)( 34,284)( 35,283)( 36,282)( 37,229)( 38,232)( 39,231)( 40,230)
( 41,237)( 42,240)( 43,239)( 44,238)( 45,233)( 46,236)( 47,235)( 48,234)
( 49,217)( 50,220)( 51,219)( 52,218)( 53,225)( 54,228)( 55,227)( 56,226)
( 57,221)( 58,224)( 59,223)( 60,222)( 61,241)( 62,244)( 63,243)( 64,242)
( 65,249)( 66,252)( 67,251)( 68,250)( 69,245)( 70,248)( 71,247)( 72,246)
( 73,309)( 74,312)( 75,311)( 76,310)( 77,305)( 78,308)( 79,307)( 80,306)
( 81,301)( 82,304)( 83,303)( 84,302)( 85,297)( 86,300)( 87,299)( 88,298)
( 89,293)( 90,296)( 91,295)( 92,294)( 93,289)( 94,292)( 95,291)( 96,290)
( 97,321)( 98,324)( 99,323)(100,322)(101,317)(102,320)(103,319)(104,318)
(105,313)(106,316)(107,315)(108,314)(109,373)(110,376)(111,375)(112,374)
(113,381)(114,384)(115,383)(116,382)(117,377)(118,380)(119,379)(120,378)
(121,361)(122,364)(123,363)(124,362)(125,369)(126,372)(127,371)(128,370)
(129,365)(130,368)(131,367)(132,366)(133,385)(134,388)(135,387)(136,386)
(137,393)(138,396)(139,395)(140,394)(141,389)(142,392)(143,391)(144,390)
(145,337)(146,340)(147,339)(148,338)(149,345)(150,348)(151,347)(152,346)
(153,341)(154,344)(155,343)(156,342)(157,325)(158,328)(159,327)(160,326)
(161,333)(162,336)(163,335)(164,334)(165,329)(166,332)(167,331)(168,330)
(169,349)(170,352)(171,351)(172,350)(173,357)(174,360)(175,359)(176,358)
(177,353)(178,356)(179,355)(180,354)(181,417)(182,420)(183,419)(184,418)
(185,413)(186,416)(187,415)(188,414)(189,409)(190,412)(191,411)(192,410)
(193,405)(194,408)(195,407)(196,406)(197,401)(198,404)(199,403)(200,402)
(201,397)(202,400)(203,399)(204,398)(205,429)(206,432)(207,431)(208,430)
(209,425)(210,428)(211,427)(212,426)(213,421)(214,424)(215,423)(216,422);;
s3 := ( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 31)( 20, 32)
( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 49, 61)( 50, 62)( 51, 63)( 52, 64)
( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 69)( 58, 70)( 59, 71)( 60, 72)
( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,103)( 92,104)
( 93,105)( 94,106)( 95,107)( 96,108)(121,133)(122,134)(123,135)(124,136)
(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)(131,143)(132,144)
(157,169)(158,170)(159,171)(160,172)(161,173)(162,174)(163,175)(164,176)
(165,177)(166,178)(167,179)(168,180)(193,205)(194,206)(195,207)(196,208)
(197,209)(198,210)(199,211)(200,212)(201,213)(202,214)(203,215)(204,216)
(217,325)(218,326)(219,327)(220,328)(221,329)(222,330)(223,331)(224,332)
(225,333)(226,334)(227,335)(228,336)(229,349)(230,350)(231,351)(232,352)
(233,353)(234,354)(235,355)(236,356)(237,357)(238,358)(239,359)(240,360)
(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)(248,344)
(249,345)(250,346)(251,347)(252,348)(253,361)(254,362)(255,363)(256,364)
(257,365)(258,366)(259,367)(260,368)(261,369)(262,370)(263,371)(264,372)
(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)(272,392)
(273,393)(274,394)(275,395)(276,396)(277,373)(278,374)(279,375)(280,376)
(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)(288,384)
(289,397)(290,398)(291,399)(292,400)(293,401)(294,402)(295,403)(296,404)
(297,405)(298,406)(299,407)(300,408)(301,421)(302,422)(303,423)(304,424)
(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)(312,432)
(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)(320,416)
(321,417)(322,418)(323,419)(324,420);;
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*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)
(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)
(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)
(430,432);
s1 := Sym(432)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 25)( 14, 26)
( 15, 28)( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)
( 23, 32)( 24, 31)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)
( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49,105)( 50,106)
( 51,108)( 52,107)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 97)( 58, 98)
( 59,100)( 60, 99)( 61, 93)( 62, 94)( 63, 96)( 64, 95)( 65, 89)( 66, 90)
( 67, 92)( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)(111,112)(113,117)
(114,118)(115,120)(116,119)(121,133)(122,134)(123,136)(124,135)(125,141)
(126,142)(127,144)(128,143)(129,137)(130,138)(131,140)(132,139)(145,189)
(146,190)(147,192)(148,191)(149,185)(150,186)(151,188)(152,187)(153,181)
(154,182)(155,184)(156,183)(157,213)(158,214)(159,216)(160,215)(161,209)
(162,210)(163,212)(164,211)(165,205)(166,206)(167,208)(168,207)(169,201)
(170,202)(171,204)(172,203)(173,197)(174,198)(175,200)(176,199)(177,193)
(178,194)(179,196)(180,195)(219,220)(221,225)(222,226)(223,228)(224,227)
(229,241)(230,242)(231,244)(232,243)(233,249)(234,250)(235,252)(236,251)
(237,245)(238,246)(239,248)(240,247)(253,297)(254,298)(255,300)(256,299)
(257,293)(258,294)(259,296)(260,295)(261,289)(262,290)(263,292)(264,291)
(265,321)(266,322)(267,324)(268,323)(269,317)(270,318)(271,320)(272,319)
(273,313)(274,314)(275,316)(276,315)(277,309)(278,310)(279,312)(280,311)
(281,305)(282,306)(283,308)(284,307)(285,301)(286,302)(287,304)(288,303)
(327,328)(329,333)(330,334)(331,336)(332,335)(337,349)(338,350)(339,352)
(340,351)(341,357)(342,358)(343,360)(344,359)(345,353)(346,354)(347,356)
(348,355)(361,405)(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)
(368,403)(369,397)(370,398)(371,400)(372,399)(373,429)(374,430)(375,432)
(376,431)(377,425)(378,426)(379,428)(380,427)(381,421)(382,422)(383,424)
(384,423)(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)
(392,415)(393,409)(394,410)(395,412)(396,411);
s2 := Sym(432)!( 1,265)( 2,268)( 3,267)( 4,266)( 5,273)( 6,276)( 7,275)
( 8,274)( 9,269)( 10,272)( 11,271)( 12,270)( 13,253)( 14,256)( 15,255)
( 16,254)( 17,261)( 18,264)( 19,263)( 20,262)( 21,257)( 22,260)( 23,259)
( 24,258)( 25,277)( 26,280)( 27,279)( 28,278)( 29,285)( 30,288)( 31,287)
( 32,286)( 33,281)( 34,284)( 35,283)( 36,282)( 37,229)( 38,232)( 39,231)
( 40,230)( 41,237)( 42,240)( 43,239)( 44,238)( 45,233)( 46,236)( 47,235)
( 48,234)( 49,217)( 50,220)( 51,219)( 52,218)( 53,225)( 54,228)( 55,227)
( 56,226)( 57,221)( 58,224)( 59,223)( 60,222)( 61,241)( 62,244)( 63,243)
( 64,242)( 65,249)( 66,252)( 67,251)( 68,250)( 69,245)( 70,248)( 71,247)
( 72,246)( 73,309)( 74,312)( 75,311)( 76,310)( 77,305)( 78,308)( 79,307)
( 80,306)( 81,301)( 82,304)( 83,303)( 84,302)( 85,297)( 86,300)( 87,299)
( 88,298)( 89,293)( 90,296)( 91,295)( 92,294)( 93,289)( 94,292)( 95,291)
( 96,290)( 97,321)( 98,324)( 99,323)(100,322)(101,317)(102,320)(103,319)
(104,318)(105,313)(106,316)(107,315)(108,314)(109,373)(110,376)(111,375)
(112,374)(113,381)(114,384)(115,383)(116,382)(117,377)(118,380)(119,379)
(120,378)(121,361)(122,364)(123,363)(124,362)(125,369)(126,372)(127,371)
(128,370)(129,365)(130,368)(131,367)(132,366)(133,385)(134,388)(135,387)
(136,386)(137,393)(138,396)(139,395)(140,394)(141,389)(142,392)(143,391)
(144,390)(145,337)(146,340)(147,339)(148,338)(149,345)(150,348)(151,347)
(152,346)(153,341)(154,344)(155,343)(156,342)(157,325)(158,328)(159,327)
(160,326)(161,333)(162,336)(163,335)(164,334)(165,329)(166,332)(167,331)
(168,330)(169,349)(170,352)(171,351)(172,350)(173,357)(174,360)(175,359)
(176,358)(177,353)(178,356)(179,355)(180,354)(181,417)(182,420)(183,419)
(184,418)(185,413)(186,416)(187,415)(188,414)(189,409)(190,412)(191,411)
(192,410)(193,405)(194,408)(195,407)(196,406)(197,401)(198,404)(199,403)
(200,402)(201,397)(202,400)(203,399)(204,398)(205,429)(206,432)(207,431)
(208,430)(209,425)(210,428)(211,427)(212,426)(213,421)(214,424)(215,423)
(216,422);
s3 := Sym(432)!( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 31)
( 20, 32)( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 49, 61)( 50, 62)( 51, 63)
( 52, 64)( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 69)( 58, 70)( 59, 71)
( 60, 72)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,103)
( 92,104)( 93,105)( 94,106)( 95,107)( 96,108)(121,133)(122,134)(123,135)
(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)(131,143)
(132,144)(157,169)(158,170)(159,171)(160,172)(161,173)(162,174)(163,175)
(164,176)(165,177)(166,178)(167,179)(168,180)(193,205)(194,206)(195,207)
(196,208)(197,209)(198,210)(199,211)(200,212)(201,213)(202,214)(203,215)
(204,216)(217,325)(218,326)(219,327)(220,328)(221,329)(222,330)(223,331)
(224,332)(225,333)(226,334)(227,335)(228,336)(229,349)(230,350)(231,351)
(232,352)(233,353)(234,354)(235,355)(236,356)(237,357)(238,358)(239,359)
(240,360)(241,337)(242,338)(243,339)(244,340)(245,341)(246,342)(247,343)
(248,344)(249,345)(250,346)(251,347)(252,348)(253,361)(254,362)(255,363)
(256,364)(257,365)(258,366)(259,367)(260,368)(261,369)(262,370)(263,371)
(264,372)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,391)
(272,392)(273,393)(274,394)(275,395)(276,396)(277,373)(278,374)(279,375)
(280,376)(281,377)(282,378)(283,379)(284,380)(285,381)(286,382)(287,383)
(288,384)(289,397)(290,398)(291,399)(292,400)(293,401)(294,402)(295,403)
(296,404)(297,405)(298,406)(299,407)(300,408)(301,421)(302,422)(303,423)
(304,424)(305,425)(306,426)(307,427)(308,428)(309,429)(310,430)(311,431)
(312,432)(313,409)(314,410)(315,411)(316,412)(317,413)(318,414)(319,415)
(320,416)(321,417)(322,418)(323,419)(324,420);
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*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope