Polytope of Type {16,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,32300)
Rank : 3
Schlafli Type : {16,4}
Number of vertices, edges, etc : 144, 288, 36
Order of s0s1s2 : 48
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,4}*576a
4-fold quotients : {4,4}*288
8-fold quotients : {4,4}*144
9-fold quotients : {16,4}*128b
16-fold quotients : {4,4}*72
18-fold quotients : {8,4}*64a
36-fold quotients : {4,4}*32, {8,2}*32
72-fold quotients : {2,4}*16, {4,2}*16
144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,433)( 2,434)( 3,435)( 4,441)( 5,439)( 6,440)( 7,437)( 8,438)
( 9,436)( 10,442)( 11,443)( 12,444)( 13,450)( 14,448)( 15,449)( 16,446)
( 17,447)( 18,445)( 19,460)( 20,461)( 21,462)( 22,468)( 23,466)( 24,467)
( 25,464)( 26,465)( 27,463)( 28,451)( 29,452)( 30,453)( 31,459)( 32,457)
( 33,458)( 34,455)( 35,456)( 36,454)( 37,478)( 38,479)( 39,480)( 40,486)
( 41,484)( 42,485)( 43,482)( 44,483)( 45,481)( 46,469)( 47,470)( 48,471)
( 49,477)( 50,475)( 51,476)( 52,473)( 53,474)( 54,472)( 55,487)( 56,488)
( 57,489)( 58,495)( 59,493)( 60,494)( 61,491)( 62,492)( 63,490)( 64,496)
( 65,497)( 66,498)( 67,504)( 68,502)( 69,503)( 70,500)( 71,501)( 72,499)
( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)( 80,537)
( 81,535)( 82,523)( 83,524)( 84,525)( 85,531)( 86,529)( 87,530)( 88,527)
( 89,528)( 90,526)( 91,514)( 92,515)( 93,516)( 94,522)( 95,520)( 96,521)
( 97,518)( 98,519)( 99,517)(100,505)(101,506)(102,507)(103,513)(104,511)
(105,512)(106,509)(107,510)(108,508)(109,559)(110,560)(111,561)(112,567)
(113,565)(114,566)(115,563)(116,564)(117,562)(118,568)(119,569)(120,570)
(121,576)(122,574)(123,575)(124,572)(125,573)(126,571)(127,541)(128,542)
(129,543)(130,549)(131,547)(132,548)(133,545)(134,546)(135,544)(136,550)
(137,551)(138,552)(139,558)(140,556)(141,557)(142,554)(143,555)(144,553)
(145,289)(146,290)(147,291)(148,297)(149,295)(150,296)(151,293)(152,294)
(153,292)(154,298)(155,299)(156,300)(157,306)(158,304)(159,305)(160,302)
(161,303)(162,301)(163,316)(164,317)(165,318)(166,324)(167,322)(168,323)
(169,320)(170,321)(171,319)(172,307)(173,308)(174,309)(175,315)(176,313)
(177,314)(178,311)(179,312)(180,310)(181,334)(182,335)(183,336)(184,342)
(185,340)(186,341)(187,338)(188,339)(189,337)(190,325)(191,326)(192,327)
(193,333)(194,331)(195,332)(196,329)(197,330)(198,328)(199,343)(200,344)
(201,345)(202,351)(203,349)(204,350)(205,347)(206,348)(207,346)(208,352)
(209,353)(210,354)(211,360)(212,358)(213,359)(214,356)(215,357)(216,355)
(217,388)(218,389)(219,390)(220,396)(221,394)(222,395)(223,392)(224,393)
(225,391)(226,379)(227,380)(228,381)(229,387)(230,385)(231,386)(232,383)
(233,384)(234,382)(235,370)(236,371)(237,372)(238,378)(239,376)(240,377)
(241,374)(242,375)(243,373)(244,361)(245,362)(246,363)(247,369)(248,367)
(249,368)(250,365)(251,366)(252,364)(253,415)(254,416)(255,417)(256,423)
(257,421)(258,422)(259,419)(260,420)(261,418)(262,424)(263,425)(264,426)
(265,432)(266,430)(267,431)(268,428)(269,429)(270,427)(271,397)(272,398)
(273,399)(274,405)(275,403)(276,404)(277,401)(278,402)(279,400)(280,406)
(281,407)(282,408)(283,414)(284,412)(285,413)(286,410)(287,411)(288,409);;
s1 := ( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 19, 28)( 20, 33)
( 21, 35)( 22, 31)( 23, 36)( 24, 29)( 25, 34)( 26, 30)( 27, 32)( 38, 42)
( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 55, 64)( 56, 69)( 57, 71)
( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73, 91)( 74, 96)
( 75, 98)( 76, 94)( 77, 99)( 78, 92)( 79, 97)( 80, 93)( 81, 95)( 82,100)
( 83,105)( 84,107)( 85,103)( 86,108)( 87,101)( 88,106)( 89,102)( 90,104)
(109,127)(110,132)(111,134)(112,130)(113,135)(114,128)(115,133)(116,129)
(117,131)(118,136)(119,141)(120,143)(121,139)(122,144)(123,137)(124,142)
(125,138)(126,140)(145,181)(146,186)(147,188)(148,184)(149,189)(150,182)
(151,187)(152,183)(153,185)(154,190)(155,195)(156,197)(157,193)(158,198)
(159,191)(160,196)(161,192)(162,194)(163,208)(164,213)(165,215)(166,211)
(167,216)(168,209)(169,214)(170,210)(171,212)(172,199)(173,204)(174,206)
(175,202)(176,207)(177,200)(178,205)(179,201)(180,203)(217,271)(218,276)
(219,278)(220,274)(221,279)(222,272)(223,277)(224,273)(225,275)(226,280)
(227,285)(228,287)(229,283)(230,288)(231,281)(232,286)(233,282)(234,284)
(235,253)(236,258)(237,260)(238,256)(239,261)(240,254)(241,259)(242,255)
(243,257)(244,262)(245,267)(246,269)(247,265)(248,270)(249,263)(250,268)
(251,264)(252,266)(289,361)(290,366)(291,368)(292,364)(293,369)(294,362)
(295,367)(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)(302,378)
(303,371)(304,376)(305,372)(306,374)(307,388)(308,393)(309,395)(310,391)
(311,396)(312,389)(313,394)(314,390)(315,392)(316,379)(317,384)(318,386)
(319,382)(320,387)(321,380)(322,385)(323,381)(324,383)(325,397)(326,402)
(327,404)(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)
(335,411)(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)
(343,424)(344,429)(345,431)(346,427)(347,432)(348,425)(349,430)(350,426)
(351,428)(352,415)(353,420)(354,422)(355,418)(356,423)(357,416)(358,421)
(359,417)(360,419)(433,550)(434,555)(435,557)(436,553)(437,558)(438,551)
(439,556)(440,552)(441,554)(442,541)(443,546)(444,548)(445,544)(446,549)
(447,542)(448,547)(449,543)(450,545)(451,559)(452,564)(453,566)(454,562)
(455,567)(456,560)(457,565)(458,561)(459,563)(460,568)(461,573)(462,575)
(463,571)(464,576)(465,569)(466,574)(467,570)(468,572)(469,514)(470,519)
(471,521)(472,517)(473,522)(474,515)(475,520)(476,516)(477,518)(478,505)
(479,510)(480,512)(481,508)(482,513)(483,506)(484,511)(485,507)(486,509)
(487,523)(488,528)(489,530)(490,526)(491,531)(492,524)(493,529)(494,525)
(495,527)(496,532)(497,537)(498,539)(499,535)(500,540)(501,533)(502,538)
(503,534)(504,536);;
s2 := ( 1,146)( 2,145)( 3,147)( 4,150)( 5,149)( 6,148)( 7,151)( 8,153)
( 9,152)( 10,155)( 11,154)( 12,156)( 13,159)( 14,158)( 15,157)( 16,160)
( 17,162)( 18,161)( 19,164)( 20,163)( 21,165)( 22,168)( 23,167)( 24,166)
( 25,169)( 26,171)( 27,170)( 28,173)( 29,172)( 30,174)( 31,177)( 32,176)
( 33,175)( 34,178)( 35,180)( 36,179)( 37,182)( 38,181)( 39,183)( 40,186)
( 41,185)( 42,184)( 43,187)( 44,189)( 45,188)( 46,191)( 47,190)( 48,192)
( 49,195)( 50,194)( 51,193)( 52,196)( 53,198)( 54,197)( 55,200)( 56,199)
( 57,201)( 58,204)( 59,203)( 60,202)( 61,205)( 62,207)( 63,206)( 64,209)
( 65,208)( 66,210)( 67,213)( 68,212)( 69,211)( 70,214)( 71,216)( 72,215)
( 73,227)( 74,226)( 75,228)( 76,231)( 77,230)( 78,229)( 79,232)( 80,234)
( 81,233)( 82,218)( 83,217)( 84,219)( 85,222)( 86,221)( 87,220)( 88,223)
( 89,225)( 90,224)( 91,245)( 92,244)( 93,246)( 94,249)( 95,248)( 96,247)
( 97,250)( 98,252)( 99,251)(100,236)(101,235)(102,237)(103,240)(104,239)
(105,238)(106,241)(107,243)(108,242)(109,263)(110,262)(111,264)(112,267)
(113,266)(114,265)(115,268)(116,270)(117,269)(118,254)(119,253)(120,255)
(121,258)(122,257)(123,256)(124,259)(125,261)(126,260)(127,281)(128,280)
(129,282)(130,285)(131,284)(132,283)(133,286)(134,288)(135,287)(136,272)
(137,271)(138,273)(139,276)(140,275)(141,274)(142,277)(143,279)(144,278)
(289,434)(290,433)(291,435)(292,438)(293,437)(294,436)(295,439)(296,441)
(297,440)(298,443)(299,442)(300,444)(301,447)(302,446)(303,445)(304,448)
(305,450)(306,449)(307,452)(308,451)(309,453)(310,456)(311,455)(312,454)
(313,457)(314,459)(315,458)(316,461)(317,460)(318,462)(319,465)(320,464)
(321,463)(322,466)(323,468)(324,467)(325,470)(326,469)(327,471)(328,474)
(329,473)(330,472)(331,475)(332,477)(333,476)(334,479)(335,478)(336,480)
(337,483)(338,482)(339,481)(340,484)(341,486)(342,485)(343,488)(344,487)
(345,489)(346,492)(347,491)(348,490)(349,493)(350,495)(351,494)(352,497)
(353,496)(354,498)(355,501)(356,500)(357,499)(358,502)(359,504)(360,503)
(361,515)(362,514)(363,516)(364,519)(365,518)(366,517)(367,520)(368,522)
(369,521)(370,506)(371,505)(372,507)(373,510)(374,509)(375,508)(376,511)
(377,513)(378,512)(379,533)(380,532)(381,534)(382,537)(383,536)(384,535)
(385,538)(386,540)(387,539)(388,524)(389,523)(390,525)(391,528)(392,527)
(393,526)(394,529)(395,531)(396,530)(397,551)(398,550)(399,552)(400,555)
(401,554)(402,553)(403,556)(404,558)(405,557)(406,542)(407,541)(408,543)
(409,546)(410,545)(411,544)(412,547)(413,549)(414,548)(415,569)(416,568)
(417,570)(418,573)(419,572)(420,571)(421,574)(422,576)(423,575)(424,560)
(425,559)(426,561)(427,564)(428,563)(429,562)(430,565)(431,567)(432,566);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(576)!( 1,433)( 2,434)( 3,435)( 4,441)( 5,439)( 6,440)( 7,437)
( 8,438)( 9,436)( 10,442)( 11,443)( 12,444)( 13,450)( 14,448)( 15,449)
( 16,446)( 17,447)( 18,445)( 19,460)( 20,461)( 21,462)( 22,468)( 23,466)
( 24,467)( 25,464)( 26,465)( 27,463)( 28,451)( 29,452)( 30,453)( 31,459)
( 32,457)( 33,458)( 34,455)( 35,456)( 36,454)( 37,478)( 38,479)( 39,480)
( 40,486)( 41,484)( 42,485)( 43,482)( 44,483)( 45,481)( 46,469)( 47,470)
( 48,471)( 49,477)( 50,475)( 51,476)( 52,473)( 53,474)( 54,472)( 55,487)
( 56,488)( 57,489)( 58,495)( 59,493)( 60,494)( 61,491)( 62,492)( 63,490)
( 64,496)( 65,497)( 66,498)( 67,504)( 68,502)( 69,503)( 70,500)( 71,501)
( 72,499)( 73,532)( 74,533)( 75,534)( 76,540)( 77,538)( 78,539)( 79,536)
( 80,537)( 81,535)( 82,523)( 83,524)( 84,525)( 85,531)( 86,529)( 87,530)
( 88,527)( 89,528)( 90,526)( 91,514)( 92,515)( 93,516)( 94,522)( 95,520)
( 96,521)( 97,518)( 98,519)( 99,517)(100,505)(101,506)(102,507)(103,513)
(104,511)(105,512)(106,509)(107,510)(108,508)(109,559)(110,560)(111,561)
(112,567)(113,565)(114,566)(115,563)(116,564)(117,562)(118,568)(119,569)
(120,570)(121,576)(122,574)(123,575)(124,572)(125,573)(126,571)(127,541)
(128,542)(129,543)(130,549)(131,547)(132,548)(133,545)(134,546)(135,544)
(136,550)(137,551)(138,552)(139,558)(140,556)(141,557)(142,554)(143,555)
(144,553)(145,289)(146,290)(147,291)(148,297)(149,295)(150,296)(151,293)
(152,294)(153,292)(154,298)(155,299)(156,300)(157,306)(158,304)(159,305)
(160,302)(161,303)(162,301)(163,316)(164,317)(165,318)(166,324)(167,322)
(168,323)(169,320)(170,321)(171,319)(172,307)(173,308)(174,309)(175,315)
(176,313)(177,314)(178,311)(179,312)(180,310)(181,334)(182,335)(183,336)
(184,342)(185,340)(186,341)(187,338)(188,339)(189,337)(190,325)(191,326)
(192,327)(193,333)(194,331)(195,332)(196,329)(197,330)(198,328)(199,343)
(200,344)(201,345)(202,351)(203,349)(204,350)(205,347)(206,348)(207,346)
(208,352)(209,353)(210,354)(211,360)(212,358)(213,359)(214,356)(215,357)
(216,355)(217,388)(218,389)(219,390)(220,396)(221,394)(222,395)(223,392)
(224,393)(225,391)(226,379)(227,380)(228,381)(229,387)(230,385)(231,386)
(232,383)(233,384)(234,382)(235,370)(236,371)(237,372)(238,378)(239,376)
(240,377)(241,374)(242,375)(243,373)(244,361)(245,362)(246,363)(247,369)
(248,367)(249,368)(250,365)(251,366)(252,364)(253,415)(254,416)(255,417)
(256,423)(257,421)(258,422)(259,419)(260,420)(261,418)(262,424)(263,425)
(264,426)(265,432)(266,430)(267,431)(268,428)(269,429)(270,427)(271,397)
(272,398)(273,399)(274,405)(275,403)(276,404)(277,401)(278,402)(279,400)
(280,406)(281,407)(282,408)(283,414)(284,412)(285,413)(286,410)(287,411)
(288,409);
s1 := Sym(576)!( 2, 6)( 3, 8)( 5, 9)( 11, 15)( 12, 17)( 14, 18)( 19, 28)
( 20, 33)( 21, 35)( 22, 31)( 23, 36)( 24, 29)( 25, 34)( 26, 30)( 27, 32)
( 38, 42)( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 55, 64)( 56, 69)
( 57, 71)( 58, 67)( 59, 72)( 60, 65)( 61, 70)( 62, 66)( 63, 68)( 73, 91)
( 74, 96)( 75, 98)( 76, 94)( 77, 99)( 78, 92)( 79, 97)( 80, 93)( 81, 95)
( 82,100)( 83,105)( 84,107)( 85,103)( 86,108)( 87,101)( 88,106)( 89,102)
( 90,104)(109,127)(110,132)(111,134)(112,130)(113,135)(114,128)(115,133)
(116,129)(117,131)(118,136)(119,141)(120,143)(121,139)(122,144)(123,137)
(124,142)(125,138)(126,140)(145,181)(146,186)(147,188)(148,184)(149,189)
(150,182)(151,187)(152,183)(153,185)(154,190)(155,195)(156,197)(157,193)
(158,198)(159,191)(160,196)(161,192)(162,194)(163,208)(164,213)(165,215)
(166,211)(167,216)(168,209)(169,214)(170,210)(171,212)(172,199)(173,204)
(174,206)(175,202)(176,207)(177,200)(178,205)(179,201)(180,203)(217,271)
(218,276)(219,278)(220,274)(221,279)(222,272)(223,277)(224,273)(225,275)
(226,280)(227,285)(228,287)(229,283)(230,288)(231,281)(232,286)(233,282)
(234,284)(235,253)(236,258)(237,260)(238,256)(239,261)(240,254)(241,259)
(242,255)(243,257)(244,262)(245,267)(246,269)(247,265)(248,270)(249,263)
(250,268)(251,264)(252,266)(289,361)(290,366)(291,368)(292,364)(293,369)
(294,362)(295,367)(296,363)(297,365)(298,370)(299,375)(300,377)(301,373)
(302,378)(303,371)(304,376)(305,372)(306,374)(307,388)(308,393)(309,395)
(310,391)(311,396)(312,389)(313,394)(314,390)(315,392)(316,379)(317,384)
(318,386)(319,382)(320,387)(321,380)(322,385)(323,381)(324,383)(325,397)
(326,402)(327,404)(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)
(334,406)(335,411)(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)
(342,410)(343,424)(344,429)(345,431)(346,427)(347,432)(348,425)(349,430)
(350,426)(351,428)(352,415)(353,420)(354,422)(355,418)(356,423)(357,416)
(358,421)(359,417)(360,419)(433,550)(434,555)(435,557)(436,553)(437,558)
(438,551)(439,556)(440,552)(441,554)(442,541)(443,546)(444,548)(445,544)
(446,549)(447,542)(448,547)(449,543)(450,545)(451,559)(452,564)(453,566)
(454,562)(455,567)(456,560)(457,565)(458,561)(459,563)(460,568)(461,573)
(462,575)(463,571)(464,576)(465,569)(466,574)(467,570)(468,572)(469,514)
(470,519)(471,521)(472,517)(473,522)(474,515)(475,520)(476,516)(477,518)
(478,505)(479,510)(480,512)(481,508)(482,513)(483,506)(484,511)(485,507)
(486,509)(487,523)(488,528)(489,530)(490,526)(491,531)(492,524)(493,529)
(494,525)(495,527)(496,532)(497,537)(498,539)(499,535)(500,540)(501,533)
(502,538)(503,534)(504,536);
s2 := Sym(576)!( 1,146)( 2,145)( 3,147)( 4,150)( 5,149)( 6,148)( 7,151)
( 8,153)( 9,152)( 10,155)( 11,154)( 12,156)( 13,159)( 14,158)( 15,157)
( 16,160)( 17,162)( 18,161)( 19,164)( 20,163)( 21,165)( 22,168)( 23,167)
( 24,166)( 25,169)( 26,171)( 27,170)( 28,173)( 29,172)( 30,174)( 31,177)
( 32,176)( 33,175)( 34,178)( 35,180)( 36,179)( 37,182)( 38,181)( 39,183)
( 40,186)( 41,185)( 42,184)( 43,187)( 44,189)( 45,188)( 46,191)( 47,190)
( 48,192)( 49,195)( 50,194)( 51,193)( 52,196)( 53,198)( 54,197)( 55,200)
( 56,199)( 57,201)( 58,204)( 59,203)( 60,202)( 61,205)( 62,207)( 63,206)
( 64,209)( 65,208)( 66,210)( 67,213)( 68,212)( 69,211)( 70,214)( 71,216)
( 72,215)( 73,227)( 74,226)( 75,228)( 76,231)( 77,230)( 78,229)( 79,232)
( 80,234)( 81,233)( 82,218)( 83,217)( 84,219)( 85,222)( 86,221)( 87,220)
( 88,223)( 89,225)( 90,224)( 91,245)( 92,244)( 93,246)( 94,249)( 95,248)
( 96,247)( 97,250)( 98,252)( 99,251)(100,236)(101,235)(102,237)(103,240)
(104,239)(105,238)(106,241)(107,243)(108,242)(109,263)(110,262)(111,264)
(112,267)(113,266)(114,265)(115,268)(116,270)(117,269)(118,254)(119,253)
(120,255)(121,258)(122,257)(123,256)(124,259)(125,261)(126,260)(127,281)
(128,280)(129,282)(130,285)(131,284)(132,283)(133,286)(134,288)(135,287)
(136,272)(137,271)(138,273)(139,276)(140,275)(141,274)(142,277)(143,279)
(144,278)(289,434)(290,433)(291,435)(292,438)(293,437)(294,436)(295,439)
(296,441)(297,440)(298,443)(299,442)(300,444)(301,447)(302,446)(303,445)
(304,448)(305,450)(306,449)(307,452)(308,451)(309,453)(310,456)(311,455)
(312,454)(313,457)(314,459)(315,458)(316,461)(317,460)(318,462)(319,465)
(320,464)(321,463)(322,466)(323,468)(324,467)(325,470)(326,469)(327,471)
(328,474)(329,473)(330,472)(331,475)(332,477)(333,476)(334,479)(335,478)
(336,480)(337,483)(338,482)(339,481)(340,484)(341,486)(342,485)(343,488)
(344,487)(345,489)(346,492)(347,491)(348,490)(349,493)(350,495)(351,494)
(352,497)(353,496)(354,498)(355,501)(356,500)(357,499)(358,502)(359,504)
(360,503)(361,515)(362,514)(363,516)(364,519)(365,518)(366,517)(367,520)
(368,522)(369,521)(370,506)(371,505)(372,507)(373,510)(374,509)(375,508)
(376,511)(377,513)(378,512)(379,533)(380,532)(381,534)(382,537)(383,536)
(384,535)(385,538)(386,540)(387,539)(388,524)(389,523)(390,525)(391,528)
(392,527)(393,526)(394,529)(395,531)(396,530)(397,551)(398,550)(399,552)
(400,555)(401,554)(402,553)(403,556)(404,558)(405,557)(406,542)(407,541)
(408,543)(409,546)(410,545)(411,544)(412,547)(413,549)(414,548)(415,569)
(416,568)(417,570)(418,573)(419,572)(420,571)(421,574)(422,576)(423,575)
(424,560)(425,559)(426,561)(427,564)(428,563)(429,562)(430,565)(431,567)
(432,566);
poly := sub<Sym(576)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0 >;
References : None.
to this polytope