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