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Polytope of Type {4,14,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,14,8}*896
Also Known As : {{4,14|2},{14,8|2}}. if this polytope has another name.
Group : SmallGroup(896,12235)
Rank : 4
Schlafli Type : {4,14,8}
Number of vertices, edges, etc : 4, 28, 56, 8
Order of s0s1s2s3 : 56
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,14,8,2} of size 1792
Vertex Figure Of :
   {2,4,14,8} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,14,4}*448, {2,14,8}*448
   4-fold quotients : {2,14,4}*224, {4,14,2}*224
   7-fold quotients : {4,2,8}*128
   8-fold quotients : {2,14,2}*112
   14-fold quotients : {4,2,4}*64, {2,2,8}*64
   16-fold quotients : {2,7,2}*56
   28-fold quotients : {2,2,4}*32, {4,2,2}*32
   56-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,14,8}*1792, {4,28,8}*1792a, {4,14,16}*1792
Permutation Representation (GAP) :
s0 := (  1,113)(  2,114)(  3,115)(  4,116)(  5,117)(  6,118)(  7,119)(  8,120)
(  9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)
( 17,129)( 18,130)( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)( 24,136)
( 25,137)( 26,138)( 27,139)( 28,140)( 29,141)( 30,142)( 31,143)( 32,144)
( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)( 40,152)
( 41,153)( 42,154)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)( 48,160)
( 49,161)( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)( 56,168)
( 57,169)( 58,170)( 59,171)( 60,172)( 61,173)( 62,174)( 63,175)( 64,176)
( 65,177)( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)( 72,184)
( 73,185)( 74,186)( 75,187)( 76,188)( 77,189)( 78,190)( 79,191)( 80,192)
( 81,193)( 82,194)( 83,195)( 84,196)( 85,197)( 86,198)( 87,199)( 88,200)
( 89,201)( 90,202)( 91,203)( 92,204)( 93,205)( 94,206)( 95,207)( 96,208)
( 97,209)( 98,210)( 99,211)(100,212)(101,213)(102,214)(103,215)(104,216)
(105,217)(106,218)(107,219)(108,220)(109,221)(110,222)(111,223)(112,224)
(225,337)(226,338)(227,339)(228,340)(229,341)(230,342)(231,343)(232,344)
(233,345)(234,346)(235,347)(236,348)(237,349)(238,350)(239,351)(240,352)
(241,353)(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)(248,360)
(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)(256,368)
(257,369)(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)(264,376)
(265,377)(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)(272,384)
(273,385)(274,386)(275,387)(276,388)(277,389)(278,390)(279,391)(280,392)
(281,393)(282,394)(283,395)(284,396)(285,397)(286,398)(287,399)(288,400)
(289,401)(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)(296,408)
(297,409)(298,410)(299,411)(300,412)(301,413)(302,414)(303,415)(304,416)
(305,417)(306,418)(307,419)(308,420)(309,421)(310,422)(311,423)(312,424)
(313,425)(314,426)(315,427)(316,428)(317,429)(318,430)(319,431)(320,432)
(321,433)(322,434)(323,435)(324,436)(325,437)(326,438)(327,439)(328,440)
(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)(336,448);;
s1 := (  1, 85)(  2, 91)(  3, 90)(  4, 89)(  5, 88)(  6, 87)(  7, 86)(  8, 92)
(  9, 98)( 10, 97)( 11, 96)( 12, 95)( 13, 94)( 14, 93)( 15, 99)( 16,105)
( 17,104)( 18,103)( 19,102)( 20,101)( 21,100)( 22,106)( 23,112)( 24,111)
( 25,110)( 26,109)( 27,108)( 28,107)( 29, 64)( 30, 70)( 31, 69)( 32, 68)
( 33, 67)( 34, 66)( 35, 65)( 36, 57)( 37, 63)( 38, 62)( 39, 61)( 40, 60)
( 41, 59)( 42, 58)( 43, 78)( 44, 84)( 45, 83)( 46, 82)( 47, 81)( 48, 80)
( 49, 79)( 50, 71)( 51, 77)( 52, 76)( 53, 75)( 54, 74)( 55, 73)( 56, 72)
(113,211)(114,217)(115,216)(116,215)(117,214)(118,213)(119,212)(120,218)
(121,224)(122,223)(123,222)(124,221)(125,220)(126,219)(127,197)(128,203)
(129,202)(130,201)(131,200)(132,199)(133,198)(134,204)(135,210)(136,209)
(137,208)(138,207)(139,206)(140,205)(141,190)(142,196)(143,195)(144,194)
(145,193)(146,192)(147,191)(148,183)(149,189)(150,188)(151,187)(152,186)
(153,185)(154,184)(155,176)(156,182)(157,181)(158,180)(159,179)(160,178)
(161,177)(162,169)(163,175)(164,174)(165,173)(166,172)(167,171)(168,170)
(225,281)(226,287)(227,286)(228,285)(229,284)(230,283)(231,282)(232,288)
(233,294)(234,293)(235,292)(236,291)(237,290)(238,289)(239,295)(240,301)
(241,300)(242,299)(243,298)(244,297)(245,296)(246,302)(247,308)(248,307)
(249,306)(250,305)(251,304)(252,303)(253,309)(254,315)(255,314)(256,313)
(257,312)(258,311)(259,310)(260,316)(261,322)(262,321)(263,320)(264,319)
(265,318)(266,317)(267,323)(268,329)(269,328)(270,327)(271,326)(272,325)
(273,324)(274,330)(275,336)(276,335)(277,334)(278,333)(279,332)(280,331)
(337,407)(338,413)(339,412)(340,411)(341,410)(342,409)(343,408)(344,414)
(345,420)(346,419)(347,418)(348,417)(349,416)(350,415)(351,393)(352,399)
(353,398)(354,397)(355,396)(356,395)(357,394)(358,400)(359,406)(360,405)
(361,404)(362,403)(363,402)(364,401)(365,435)(366,441)(367,440)(368,439)
(369,438)(370,437)(371,436)(372,442)(373,448)(374,447)(375,446)(376,445)
(377,444)(378,443)(379,421)(380,427)(381,426)(382,425)(383,424)(384,423)
(385,422)(386,428)(387,434)(388,433)(389,432)(390,431)(391,430)(392,429);;
s2 := (  1,226)(  2,225)(  3,231)(  4,230)(  5,229)(  6,228)(  7,227)(  8,233)
(  9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,240)( 16,239)
( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,247)( 23,246)( 24,252)
( 25,251)( 26,250)( 27,249)( 28,248)( 29,261)( 30,260)( 31,266)( 32,265)
( 33,264)( 34,263)( 35,262)( 36,254)( 37,253)( 38,259)( 39,258)( 40,257)
( 41,256)( 42,255)( 43,275)( 44,274)( 45,280)( 46,279)( 47,278)( 48,277)
( 49,276)( 50,268)( 51,267)( 52,273)( 53,272)( 54,271)( 55,270)( 56,269)
( 57,310)( 58,309)( 59,315)( 60,314)( 61,313)( 62,312)( 63,311)( 64,317)
( 65,316)( 66,322)( 67,321)( 68,320)( 69,319)( 70,318)( 71,324)( 72,323)
( 73,329)( 74,328)( 75,327)( 76,326)( 77,325)( 78,331)( 79,330)( 80,336)
( 81,335)( 82,334)( 83,333)( 84,332)( 85,282)( 86,281)( 87,287)( 88,286)
( 89,285)( 90,284)( 91,283)( 92,289)( 93,288)( 94,294)( 95,293)( 96,292)
( 97,291)( 98,290)( 99,296)(100,295)(101,301)(102,300)(103,299)(104,298)
(105,297)(106,303)(107,302)(108,308)(109,307)(110,306)(111,305)(112,304)
(113,338)(114,337)(115,343)(116,342)(117,341)(118,340)(119,339)(120,345)
(121,344)(122,350)(123,349)(124,348)(125,347)(126,346)(127,352)(128,351)
(129,357)(130,356)(131,355)(132,354)(133,353)(134,359)(135,358)(136,364)
(137,363)(138,362)(139,361)(140,360)(141,373)(142,372)(143,378)(144,377)
(145,376)(146,375)(147,374)(148,366)(149,365)(150,371)(151,370)(152,369)
(153,368)(154,367)(155,387)(156,386)(157,392)(158,391)(159,390)(160,389)
(161,388)(162,380)(163,379)(164,385)(165,384)(166,383)(167,382)(168,381)
(169,422)(170,421)(171,427)(172,426)(173,425)(174,424)(175,423)(176,429)
(177,428)(178,434)(179,433)(180,432)(181,431)(182,430)(183,436)(184,435)
(185,441)(186,440)(187,439)(188,438)(189,437)(190,443)(191,442)(192,448)
(193,447)(194,446)(195,445)(196,444)(197,394)(198,393)(199,399)(200,398)
(201,397)(202,396)(203,395)(204,401)(205,400)(206,406)(207,405)(208,404)
(209,403)(210,402)(211,408)(212,407)(213,413)(214,412)(215,411)(216,410)
(217,409)(218,415)(219,414)(220,420)(221,419)(222,418)(223,417)(224,416);;
s3 := (  1, 57)(  2, 58)(  3, 59)(  4, 60)(  5, 61)(  6, 62)(  7, 63)(  8, 64)
(  9, 65)( 10, 66)( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 71)( 16, 72)
( 17, 73)( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)( 24, 80)
( 25, 81)( 26, 82)( 27, 83)( 28, 84)( 29, 92)( 30, 93)( 31, 94)( 32, 95)
( 33, 96)( 34, 97)( 35, 98)( 36, 85)( 37, 86)( 38, 87)( 39, 88)( 40, 89)
( 41, 90)( 42, 91)( 43,106)( 44,107)( 45,108)( 46,109)( 47,110)( 48,111)
( 49,112)( 50, 99)( 51,100)( 52,101)( 53,102)( 54,103)( 55,104)( 56,105)
(113,169)(114,170)(115,171)(116,172)(117,173)(118,174)(119,175)(120,176)
(121,177)(122,178)(123,179)(124,180)(125,181)(126,182)(127,183)(128,184)
(129,185)(130,186)(131,187)(132,188)(133,189)(134,190)(135,191)(136,192)
(137,193)(138,194)(139,195)(140,196)(141,204)(142,205)(143,206)(144,207)
(145,208)(146,209)(147,210)(148,197)(149,198)(150,199)(151,200)(152,201)
(153,202)(154,203)(155,218)(156,219)(157,220)(158,221)(159,222)(160,223)
(161,224)(162,211)(163,212)(164,213)(165,214)(166,215)(167,216)(168,217)
(225,281)(226,282)(227,283)(228,284)(229,285)(230,286)(231,287)(232,288)
(233,289)(234,290)(235,291)(236,292)(237,293)(238,294)(239,295)(240,296)
(241,297)(242,298)(243,299)(244,300)(245,301)(246,302)(247,303)(248,304)
(249,305)(250,306)(251,307)(252,308)(253,316)(254,317)(255,318)(256,319)
(257,320)(258,321)(259,322)(260,309)(261,310)(262,311)(263,312)(264,313)
(265,314)(266,315)(267,330)(268,331)(269,332)(270,333)(271,334)(272,335)
(273,336)(274,323)(275,324)(276,325)(277,326)(278,327)(279,328)(280,329)
(337,393)(338,394)(339,395)(340,396)(341,397)(342,398)(343,399)(344,400)
(345,401)(346,402)(347,403)(348,404)(349,405)(350,406)(351,407)(352,408)
(353,409)(354,410)(355,411)(356,412)(357,413)(358,414)(359,415)(360,416)
(361,417)(362,418)(363,419)(364,420)(365,428)(366,429)(367,430)(368,431)
(369,432)(370,433)(371,434)(372,421)(373,422)(374,423)(375,424)(376,425)
(377,426)(378,427)(379,442)(380,443)(381,444)(382,445)(383,446)(384,447)
(385,448)(386,435)(387,436)(388,437)(389,438)(390,439)(391,440)(392,441);;
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*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(448)!(  1,113)(  2,114)(  3,115)(  4,116)(  5,117)(  6,118)(  7,119)
(  8,120)(  9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)
( 16,128)( 17,129)( 18,130)( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)
( 24,136)( 25,137)( 26,138)( 27,139)( 28,140)( 29,141)( 30,142)( 31,143)
( 32,144)( 33,145)( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)
( 40,152)( 41,153)( 42,154)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)
( 48,160)( 49,161)( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)
( 56,168)( 57,169)( 58,170)( 59,171)( 60,172)( 61,173)( 62,174)( 63,175)
( 64,176)( 65,177)( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)
( 72,184)( 73,185)( 74,186)( 75,187)( 76,188)( 77,189)( 78,190)( 79,191)
( 80,192)( 81,193)( 82,194)( 83,195)( 84,196)( 85,197)( 86,198)( 87,199)
( 88,200)( 89,201)( 90,202)( 91,203)( 92,204)( 93,205)( 94,206)( 95,207)
( 96,208)( 97,209)( 98,210)( 99,211)(100,212)(101,213)(102,214)(103,215)
(104,216)(105,217)(106,218)(107,219)(108,220)(109,221)(110,222)(111,223)
(112,224)(225,337)(226,338)(227,339)(228,340)(229,341)(230,342)(231,343)
(232,344)(233,345)(234,346)(235,347)(236,348)(237,349)(238,350)(239,351)
(240,352)(241,353)(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)
(248,360)(249,361)(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)
(256,368)(257,369)(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)
(264,376)(265,377)(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)
(272,384)(273,385)(274,386)(275,387)(276,388)(277,389)(278,390)(279,391)
(280,392)(281,393)(282,394)(283,395)(284,396)(285,397)(286,398)(287,399)
(288,400)(289,401)(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)
(296,408)(297,409)(298,410)(299,411)(300,412)(301,413)(302,414)(303,415)
(304,416)(305,417)(306,418)(307,419)(308,420)(309,421)(310,422)(311,423)
(312,424)(313,425)(314,426)(315,427)(316,428)(317,429)(318,430)(319,431)
(320,432)(321,433)(322,434)(323,435)(324,436)(325,437)(326,438)(327,439)
(328,440)(329,441)(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)
(336,448);
s1 := Sym(448)!(  1, 85)(  2, 91)(  3, 90)(  4, 89)(  5, 88)(  6, 87)(  7, 86)
(  8, 92)(  9, 98)( 10, 97)( 11, 96)( 12, 95)( 13, 94)( 14, 93)( 15, 99)
( 16,105)( 17,104)( 18,103)( 19,102)( 20,101)( 21,100)( 22,106)( 23,112)
( 24,111)( 25,110)( 26,109)( 27,108)( 28,107)( 29, 64)( 30, 70)( 31, 69)
( 32, 68)( 33, 67)( 34, 66)( 35, 65)( 36, 57)( 37, 63)( 38, 62)( 39, 61)
( 40, 60)( 41, 59)( 42, 58)( 43, 78)( 44, 84)( 45, 83)( 46, 82)( 47, 81)
( 48, 80)( 49, 79)( 50, 71)( 51, 77)( 52, 76)( 53, 75)( 54, 74)( 55, 73)
( 56, 72)(113,211)(114,217)(115,216)(116,215)(117,214)(118,213)(119,212)
(120,218)(121,224)(122,223)(123,222)(124,221)(125,220)(126,219)(127,197)
(128,203)(129,202)(130,201)(131,200)(132,199)(133,198)(134,204)(135,210)
(136,209)(137,208)(138,207)(139,206)(140,205)(141,190)(142,196)(143,195)
(144,194)(145,193)(146,192)(147,191)(148,183)(149,189)(150,188)(151,187)
(152,186)(153,185)(154,184)(155,176)(156,182)(157,181)(158,180)(159,179)
(160,178)(161,177)(162,169)(163,175)(164,174)(165,173)(166,172)(167,171)
(168,170)(225,281)(226,287)(227,286)(228,285)(229,284)(230,283)(231,282)
(232,288)(233,294)(234,293)(235,292)(236,291)(237,290)(238,289)(239,295)
(240,301)(241,300)(242,299)(243,298)(244,297)(245,296)(246,302)(247,308)
(248,307)(249,306)(250,305)(251,304)(252,303)(253,309)(254,315)(255,314)
(256,313)(257,312)(258,311)(259,310)(260,316)(261,322)(262,321)(263,320)
(264,319)(265,318)(266,317)(267,323)(268,329)(269,328)(270,327)(271,326)
(272,325)(273,324)(274,330)(275,336)(276,335)(277,334)(278,333)(279,332)
(280,331)(337,407)(338,413)(339,412)(340,411)(341,410)(342,409)(343,408)
(344,414)(345,420)(346,419)(347,418)(348,417)(349,416)(350,415)(351,393)
(352,399)(353,398)(354,397)(355,396)(356,395)(357,394)(358,400)(359,406)
(360,405)(361,404)(362,403)(363,402)(364,401)(365,435)(366,441)(367,440)
(368,439)(369,438)(370,437)(371,436)(372,442)(373,448)(374,447)(375,446)
(376,445)(377,444)(378,443)(379,421)(380,427)(381,426)(382,425)(383,424)
(384,423)(385,422)(386,428)(387,434)(388,433)(389,432)(390,431)(391,430)
(392,429);
s2 := Sym(448)!(  1,226)(  2,225)(  3,231)(  4,230)(  5,229)(  6,228)(  7,227)
(  8,233)(  9,232)( 10,238)( 11,237)( 12,236)( 13,235)( 14,234)( 15,240)
( 16,239)( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,247)( 23,246)
( 24,252)( 25,251)( 26,250)( 27,249)( 28,248)( 29,261)( 30,260)( 31,266)
( 32,265)( 33,264)( 34,263)( 35,262)( 36,254)( 37,253)( 38,259)( 39,258)
( 40,257)( 41,256)( 42,255)( 43,275)( 44,274)( 45,280)( 46,279)( 47,278)
( 48,277)( 49,276)( 50,268)( 51,267)( 52,273)( 53,272)( 54,271)( 55,270)
( 56,269)( 57,310)( 58,309)( 59,315)( 60,314)( 61,313)( 62,312)( 63,311)
( 64,317)( 65,316)( 66,322)( 67,321)( 68,320)( 69,319)( 70,318)( 71,324)
( 72,323)( 73,329)( 74,328)( 75,327)( 76,326)( 77,325)( 78,331)( 79,330)
( 80,336)( 81,335)( 82,334)( 83,333)( 84,332)( 85,282)( 86,281)( 87,287)
( 88,286)( 89,285)( 90,284)( 91,283)( 92,289)( 93,288)( 94,294)( 95,293)
( 96,292)( 97,291)( 98,290)( 99,296)(100,295)(101,301)(102,300)(103,299)
(104,298)(105,297)(106,303)(107,302)(108,308)(109,307)(110,306)(111,305)
(112,304)(113,338)(114,337)(115,343)(116,342)(117,341)(118,340)(119,339)
(120,345)(121,344)(122,350)(123,349)(124,348)(125,347)(126,346)(127,352)
(128,351)(129,357)(130,356)(131,355)(132,354)(133,353)(134,359)(135,358)
(136,364)(137,363)(138,362)(139,361)(140,360)(141,373)(142,372)(143,378)
(144,377)(145,376)(146,375)(147,374)(148,366)(149,365)(150,371)(151,370)
(152,369)(153,368)(154,367)(155,387)(156,386)(157,392)(158,391)(159,390)
(160,389)(161,388)(162,380)(163,379)(164,385)(165,384)(166,383)(167,382)
(168,381)(169,422)(170,421)(171,427)(172,426)(173,425)(174,424)(175,423)
(176,429)(177,428)(178,434)(179,433)(180,432)(181,431)(182,430)(183,436)
(184,435)(185,441)(186,440)(187,439)(188,438)(189,437)(190,443)(191,442)
(192,448)(193,447)(194,446)(195,445)(196,444)(197,394)(198,393)(199,399)
(200,398)(201,397)(202,396)(203,395)(204,401)(205,400)(206,406)(207,405)
(208,404)(209,403)(210,402)(211,408)(212,407)(213,413)(214,412)(215,411)
(216,410)(217,409)(218,415)(219,414)(220,420)(221,419)(222,418)(223,417)
(224,416);
s3 := Sym(448)!(  1, 57)(  2, 58)(  3, 59)(  4, 60)(  5, 61)(  6, 62)(  7, 63)
(  8, 64)(  9, 65)( 10, 66)( 11, 67)( 12, 68)( 13, 69)( 14, 70)( 15, 71)
( 16, 72)( 17, 73)( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22, 78)( 23, 79)
( 24, 80)( 25, 81)( 26, 82)( 27, 83)( 28, 84)( 29, 92)( 30, 93)( 31, 94)
( 32, 95)( 33, 96)( 34, 97)( 35, 98)( 36, 85)( 37, 86)( 38, 87)( 39, 88)
( 40, 89)( 41, 90)( 42, 91)( 43,106)( 44,107)( 45,108)( 46,109)( 47,110)
( 48,111)( 49,112)( 50, 99)( 51,100)( 52,101)( 53,102)( 54,103)( 55,104)
( 56,105)(113,169)(114,170)(115,171)(116,172)(117,173)(118,174)(119,175)
(120,176)(121,177)(122,178)(123,179)(124,180)(125,181)(126,182)(127,183)
(128,184)(129,185)(130,186)(131,187)(132,188)(133,189)(134,190)(135,191)
(136,192)(137,193)(138,194)(139,195)(140,196)(141,204)(142,205)(143,206)
(144,207)(145,208)(146,209)(147,210)(148,197)(149,198)(150,199)(151,200)
(152,201)(153,202)(154,203)(155,218)(156,219)(157,220)(158,221)(159,222)
(160,223)(161,224)(162,211)(163,212)(164,213)(165,214)(166,215)(167,216)
(168,217)(225,281)(226,282)(227,283)(228,284)(229,285)(230,286)(231,287)
(232,288)(233,289)(234,290)(235,291)(236,292)(237,293)(238,294)(239,295)
(240,296)(241,297)(242,298)(243,299)(244,300)(245,301)(246,302)(247,303)
(248,304)(249,305)(250,306)(251,307)(252,308)(253,316)(254,317)(255,318)
(256,319)(257,320)(258,321)(259,322)(260,309)(261,310)(262,311)(263,312)
(264,313)(265,314)(266,315)(267,330)(268,331)(269,332)(270,333)(271,334)
(272,335)(273,336)(274,323)(275,324)(276,325)(277,326)(278,327)(279,328)
(280,329)(337,393)(338,394)(339,395)(340,396)(341,397)(342,398)(343,399)
(344,400)(345,401)(346,402)(347,403)(348,404)(349,405)(350,406)(351,407)
(352,408)(353,409)(354,410)(355,411)(356,412)(357,413)(358,414)(359,415)
(360,416)(361,417)(362,418)(363,419)(364,420)(365,428)(366,429)(367,430)
(368,431)(369,432)(370,433)(371,434)(372,421)(373,422)(374,423)(375,424)
(376,425)(377,426)(378,427)(379,442)(380,443)(381,444)(382,445)(383,446)
(384,447)(385,448)(386,435)(387,436)(388,437)(389,438)(390,439)(391,440)
(392,441);
poly := sub<Sym(448)|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*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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