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Polytope of Type {2,28,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,28,16}*1792a
if this polytope has a name.
Group : SmallGroup(1792,323305)
Rank : 4
Schlafli Type : {2,28,16}
Number of vertices, edges, etc : 2, 28, 224, 16
Order of s0s1s2s3 : 112
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,28,8}*896a, {2,14,16}*896
   4-fold quotients : {2,28,4}*448, {2,14,8}*448
   7-fold quotients : {2,4,16}*256a
   8-fold quotients : {2,28,2}*224, {2,14,4}*224
   14-fold quotients : {2,4,8}*128a, {2,2,16}*128
   16-fold quotients : {2,14,2}*112
   28-fold quotients : {2,4,4}*64, {2,2,8}*64
   32-fold quotients : {2,7,2}*56
   56-fold quotients : {2,2,4}*32, {2,4,2}*32
   112-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3,115)(  4,121)(  5,120)(  6,119)(  7,118)(  8,117)(  9,116)( 10,122)
( 11,128)( 12,127)( 13,126)( 14,125)( 15,124)( 16,123)( 17,129)( 18,135)
( 19,134)( 20,133)( 21,132)( 22,131)( 23,130)( 24,136)( 25,142)( 26,141)
( 27,140)( 28,139)( 29,138)( 30,137)( 31,143)( 32,149)( 33,148)( 34,147)
( 35,146)( 36,145)( 37,144)( 38,150)( 39,156)( 40,155)( 41,154)( 42,153)
( 43,152)( 44,151)( 45,157)( 46,163)( 47,162)( 48,161)( 49,160)( 50,159)
( 51,158)( 52,164)( 53,170)( 54,169)( 55,168)( 56,167)( 57,166)( 58,165)
( 59,171)( 60,177)( 61,176)( 62,175)( 63,174)( 64,173)( 65,172)( 66,178)
( 67,184)( 68,183)( 69,182)( 70,181)( 71,180)( 72,179)( 73,185)( 74,191)
( 75,190)( 76,189)( 77,188)( 78,187)( 79,186)( 80,192)( 81,198)( 82,197)
( 83,196)( 84,195)( 85,194)( 86,193)( 87,199)( 88,205)( 89,204)( 90,203)
( 91,202)( 92,201)( 93,200)( 94,206)( 95,212)( 96,211)( 97,210)( 98,209)
( 99,208)(100,207)(101,213)(102,219)(103,218)(104,217)(105,216)(106,215)
(107,214)(108,220)(109,226)(110,225)(111,224)(112,223)(113,222)(114,221)
(227,339)(228,345)(229,344)(230,343)(231,342)(232,341)(233,340)(234,346)
(235,352)(236,351)(237,350)(238,349)(239,348)(240,347)(241,353)(242,359)
(243,358)(244,357)(245,356)(246,355)(247,354)(248,360)(249,366)(250,365)
(251,364)(252,363)(253,362)(254,361)(255,367)(256,373)(257,372)(258,371)
(259,370)(260,369)(261,368)(262,374)(263,380)(264,379)(265,378)(266,377)
(267,376)(268,375)(269,381)(270,387)(271,386)(272,385)(273,384)(274,383)
(275,382)(276,388)(277,394)(278,393)(279,392)(280,391)(281,390)(282,389)
(283,395)(284,401)(285,400)(286,399)(287,398)(288,397)(289,396)(290,402)
(291,408)(292,407)(293,406)(294,405)(295,404)(296,403)(297,409)(298,415)
(299,414)(300,413)(301,412)(302,411)(303,410)(304,416)(305,422)(306,421)
(307,420)(308,419)(309,418)(310,417)(311,423)(312,429)(313,428)(314,427)
(315,426)(316,425)(317,424)(318,430)(319,436)(320,435)(321,434)(322,433)
(323,432)(324,431)(325,437)(326,443)(327,442)(328,441)(329,440)(330,439)
(331,438)(332,444)(333,450)(334,449)(335,448)(336,447)(337,446)(338,445);;
s2 := (  3,  4)(  5,  9)(  6,  8)( 10, 11)( 12, 16)( 13, 15)( 17, 25)( 18, 24)
( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 31, 32)( 33, 37)( 34, 36)
( 38, 39)( 40, 44)( 41, 43)( 45, 53)( 46, 52)( 47, 58)( 48, 57)( 49, 56)
( 50, 55)( 51, 54)( 59, 74)( 60, 73)( 61, 79)( 62, 78)( 63, 77)( 64, 76)
( 65, 75)( 66, 81)( 67, 80)( 68, 86)( 69, 85)( 70, 84)( 71, 83)( 72, 82)
( 87,102)( 88,101)( 89,107)( 90,106)( 91,105)( 92,104)( 93,103)( 94,109)
( 95,108)( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(115,144)(116,143)
(117,149)(118,148)(119,147)(120,146)(121,145)(122,151)(123,150)(124,156)
(125,155)(126,154)(127,153)(128,152)(129,165)(130,164)(131,170)(132,169)
(133,168)(134,167)(135,166)(136,158)(137,157)(138,163)(139,162)(140,161)
(141,160)(142,159)(171,214)(172,213)(173,219)(174,218)(175,217)(176,216)
(177,215)(178,221)(179,220)(180,226)(181,225)(182,224)(183,223)(184,222)
(185,200)(186,199)(187,205)(188,204)(189,203)(190,202)(191,201)(192,207)
(193,206)(194,212)(195,211)(196,210)(197,209)(198,208)(227,284)(228,283)
(229,289)(230,288)(231,287)(232,286)(233,285)(234,291)(235,290)(236,296)
(237,295)(238,294)(239,293)(240,292)(241,305)(242,304)(243,310)(244,309)
(245,308)(246,307)(247,306)(248,298)(249,297)(250,303)(251,302)(252,301)
(253,300)(254,299)(255,312)(256,311)(257,317)(258,316)(259,315)(260,314)
(261,313)(262,319)(263,318)(264,324)(265,323)(266,322)(267,321)(268,320)
(269,333)(270,332)(271,338)(272,337)(273,336)(274,335)(275,334)(276,326)
(277,325)(278,331)(279,330)(280,329)(281,328)(282,327)(339,424)(340,423)
(341,429)(342,428)(343,427)(344,426)(345,425)(346,431)(347,430)(348,436)
(349,435)(350,434)(351,433)(352,432)(353,445)(354,444)(355,450)(356,449)
(357,448)(358,447)(359,446)(360,438)(361,437)(362,443)(363,442)(364,441)
(365,440)(366,439)(367,396)(368,395)(369,401)(370,400)(371,399)(372,398)
(373,397)(374,403)(375,402)(376,408)(377,407)(378,406)(379,405)(380,404)
(381,417)(382,416)(383,422)(384,421)(385,420)(386,419)(387,418)(388,410)
(389,409)(390,415)(391,414)(392,413)(393,412)(394,411);;
s3 := (  3,227)(  4,228)(  5,229)(  6,230)(  7,231)(  8,232)(  9,233)( 10,234)
( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)( 17,248)( 18,249)
( 19,250)( 20,251)( 21,252)( 22,253)( 23,254)( 24,241)( 25,242)( 26,243)
( 27,244)( 28,245)( 29,246)( 30,247)( 31,255)( 32,256)( 33,257)( 34,258)
( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)( 40,264)( 41,265)( 42,266)
( 43,267)( 44,268)( 45,276)( 46,277)( 47,278)( 48,279)( 49,280)( 50,281)
( 51,282)( 52,269)( 53,270)( 54,271)( 55,272)( 56,273)( 57,274)( 58,275)
( 59,297)( 60,298)( 61,299)( 62,300)( 63,301)( 64,302)( 65,303)( 66,304)
( 67,305)( 68,306)( 69,307)( 70,308)( 71,309)( 72,310)( 73,283)( 74,284)
( 75,285)( 76,286)( 77,287)( 78,288)( 79,289)( 80,290)( 81,291)( 82,292)
( 83,293)( 84,294)( 85,295)( 86,296)( 87,325)( 88,326)( 89,327)( 90,328)
( 91,329)( 92,330)( 93,331)( 94,332)( 95,333)( 96,334)( 97,335)( 98,336)
( 99,337)(100,338)(101,311)(102,312)(103,313)(104,314)(105,315)(106,316)
(107,317)(108,318)(109,319)(110,320)(111,321)(112,322)(113,323)(114,324)
(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)(121,345)(122,346)
(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)(129,360)(130,361)
(131,362)(132,363)(133,364)(134,365)(135,366)(136,353)(137,354)(138,355)
(139,356)(140,357)(141,358)(142,359)(143,367)(144,368)(145,369)(146,370)
(147,371)(148,372)(149,373)(150,374)(151,375)(152,376)(153,377)(154,378)
(155,379)(156,380)(157,388)(158,389)(159,390)(160,391)(161,392)(162,393)
(163,394)(164,381)(165,382)(166,383)(167,384)(168,385)(169,386)(170,387)
(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)(177,415)(178,416)
(179,417)(180,418)(181,419)(182,420)(183,421)(184,422)(185,395)(186,396)
(187,397)(188,398)(189,399)(190,400)(191,401)(192,402)(193,403)(194,404)
(195,405)(196,406)(197,407)(198,408)(199,437)(200,438)(201,439)(202,440)
(203,441)(204,442)(205,443)(206,444)(207,445)(208,446)(209,447)(210,448)
(211,449)(212,450)(213,423)(214,424)(215,425)(216,426)(217,427)(218,428)
(219,429)(220,430)(221,431)(222,432)(223,433)(224,434)(225,435)(226,436);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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*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(450)!(1,2);
s1 := Sym(450)!(  3,115)(  4,121)(  5,120)(  6,119)(  7,118)(  8,117)(  9,116)
( 10,122)( 11,128)( 12,127)( 13,126)( 14,125)( 15,124)( 16,123)( 17,129)
( 18,135)( 19,134)( 20,133)( 21,132)( 22,131)( 23,130)( 24,136)( 25,142)
( 26,141)( 27,140)( 28,139)( 29,138)( 30,137)( 31,143)( 32,149)( 33,148)
( 34,147)( 35,146)( 36,145)( 37,144)( 38,150)( 39,156)( 40,155)( 41,154)
( 42,153)( 43,152)( 44,151)( 45,157)( 46,163)( 47,162)( 48,161)( 49,160)
( 50,159)( 51,158)( 52,164)( 53,170)( 54,169)( 55,168)( 56,167)( 57,166)
( 58,165)( 59,171)( 60,177)( 61,176)( 62,175)( 63,174)( 64,173)( 65,172)
( 66,178)( 67,184)( 68,183)( 69,182)( 70,181)( 71,180)( 72,179)( 73,185)
( 74,191)( 75,190)( 76,189)( 77,188)( 78,187)( 79,186)( 80,192)( 81,198)
( 82,197)( 83,196)( 84,195)( 85,194)( 86,193)( 87,199)( 88,205)( 89,204)
( 90,203)( 91,202)( 92,201)( 93,200)( 94,206)( 95,212)( 96,211)( 97,210)
( 98,209)( 99,208)(100,207)(101,213)(102,219)(103,218)(104,217)(105,216)
(106,215)(107,214)(108,220)(109,226)(110,225)(111,224)(112,223)(113,222)
(114,221)(227,339)(228,345)(229,344)(230,343)(231,342)(232,341)(233,340)
(234,346)(235,352)(236,351)(237,350)(238,349)(239,348)(240,347)(241,353)
(242,359)(243,358)(244,357)(245,356)(246,355)(247,354)(248,360)(249,366)
(250,365)(251,364)(252,363)(253,362)(254,361)(255,367)(256,373)(257,372)
(258,371)(259,370)(260,369)(261,368)(262,374)(263,380)(264,379)(265,378)
(266,377)(267,376)(268,375)(269,381)(270,387)(271,386)(272,385)(273,384)
(274,383)(275,382)(276,388)(277,394)(278,393)(279,392)(280,391)(281,390)
(282,389)(283,395)(284,401)(285,400)(286,399)(287,398)(288,397)(289,396)
(290,402)(291,408)(292,407)(293,406)(294,405)(295,404)(296,403)(297,409)
(298,415)(299,414)(300,413)(301,412)(302,411)(303,410)(304,416)(305,422)
(306,421)(307,420)(308,419)(309,418)(310,417)(311,423)(312,429)(313,428)
(314,427)(315,426)(316,425)(317,424)(318,430)(319,436)(320,435)(321,434)
(322,433)(323,432)(324,431)(325,437)(326,443)(327,442)(328,441)(329,440)
(330,439)(331,438)(332,444)(333,450)(334,449)(335,448)(336,447)(337,446)
(338,445);
s2 := Sym(450)!(  3,  4)(  5,  9)(  6,  8)( 10, 11)( 12, 16)( 13, 15)( 17, 25)
( 18, 24)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 31, 32)( 33, 37)
( 34, 36)( 38, 39)( 40, 44)( 41, 43)( 45, 53)( 46, 52)( 47, 58)( 48, 57)
( 49, 56)( 50, 55)( 51, 54)( 59, 74)( 60, 73)( 61, 79)( 62, 78)( 63, 77)
( 64, 76)( 65, 75)( 66, 81)( 67, 80)( 68, 86)( 69, 85)( 70, 84)( 71, 83)
( 72, 82)( 87,102)( 88,101)( 89,107)( 90,106)( 91,105)( 92,104)( 93,103)
( 94,109)( 95,108)( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(115,144)
(116,143)(117,149)(118,148)(119,147)(120,146)(121,145)(122,151)(123,150)
(124,156)(125,155)(126,154)(127,153)(128,152)(129,165)(130,164)(131,170)
(132,169)(133,168)(134,167)(135,166)(136,158)(137,157)(138,163)(139,162)
(140,161)(141,160)(142,159)(171,214)(172,213)(173,219)(174,218)(175,217)
(176,216)(177,215)(178,221)(179,220)(180,226)(181,225)(182,224)(183,223)
(184,222)(185,200)(186,199)(187,205)(188,204)(189,203)(190,202)(191,201)
(192,207)(193,206)(194,212)(195,211)(196,210)(197,209)(198,208)(227,284)
(228,283)(229,289)(230,288)(231,287)(232,286)(233,285)(234,291)(235,290)
(236,296)(237,295)(238,294)(239,293)(240,292)(241,305)(242,304)(243,310)
(244,309)(245,308)(246,307)(247,306)(248,298)(249,297)(250,303)(251,302)
(252,301)(253,300)(254,299)(255,312)(256,311)(257,317)(258,316)(259,315)
(260,314)(261,313)(262,319)(263,318)(264,324)(265,323)(266,322)(267,321)
(268,320)(269,333)(270,332)(271,338)(272,337)(273,336)(274,335)(275,334)
(276,326)(277,325)(278,331)(279,330)(280,329)(281,328)(282,327)(339,424)
(340,423)(341,429)(342,428)(343,427)(344,426)(345,425)(346,431)(347,430)
(348,436)(349,435)(350,434)(351,433)(352,432)(353,445)(354,444)(355,450)
(356,449)(357,448)(358,447)(359,446)(360,438)(361,437)(362,443)(363,442)
(364,441)(365,440)(366,439)(367,396)(368,395)(369,401)(370,400)(371,399)
(372,398)(373,397)(374,403)(375,402)(376,408)(377,407)(378,406)(379,405)
(380,404)(381,417)(382,416)(383,422)(384,421)(385,420)(386,419)(387,418)
(388,410)(389,409)(390,415)(391,414)(392,413)(393,412)(394,411);
s3 := Sym(450)!(  3,227)(  4,228)(  5,229)(  6,230)(  7,231)(  8,232)(  9,233)
( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)( 17,248)
( 18,249)( 19,250)( 20,251)( 21,252)( 22,253)( 23,254)( 24,241)( 25,242)
( 26,243)( 27,244)( 28,245)( 29,246)( 30,247)( 31,255)( 32,256)( 33,257)
( 34,258)( 35,259)( 36,260)( 37,261)( 38,262)( 39,263)( 40,264)( 41,265)
( 42,266)( 43,267)( 44,268)( 45,276)( 46,277)( 47,278)( 48,279)( 49,280)
( 50,281)( 51,282)( 52,269)( 53,270)( 54,271)( 55,272)( 56,273)( 57,274)
( 58,275)( 59,297)( 60,298)( 61,299)( 62,300)( 63,301)( 64,302)( 65,303)
( 66,304)( 67,305)( 68,306)( 69,307)( 70,308)( 71,309)( 72,310)( 73,283)
( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,289)( 80,290)( 81,291)
( 82,292)( 83,293)( 84,294)( 85,295)( 86,296)( 87,325)( 88,326)( 89,327)
( 90,328)( 91,329)( 92,330)( 93,331)( 94,332)( 95,333)( 96,334)( 97,335)
( 98,336)( 99,337)(100,338)(101,311)(102,312)(103,313)(104,314)(105,315)
(106,316)(107,317)(108,318)(109,319)(110,320)(111,321)(112,322)(113,323)
(114,324)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)(121,345)
(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)(129,360)
(130,361)(131,362)(132,363)(133,364)(134,365)(135,366)(136,353)(137,354)
(138,355)(139,356)(140,357)(141,358)(142,359)(143,367)(144,368)(145,369)
(146,370)(147,371)(148,372)(149,373)(150,374)(151,375)(152,376)(153,377)
(154,378)(155,379)(156,380)(157,388)(158,389)(159,390)(160,391)(161,392)
(162,393)(163,394)(164,381)(165,382)(166,383)(167,384)(168,385)(169,386)
(170,387)(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)(177,415)
(178,416)(179,417)(180,418)(181,419)(182,420)(183,421)(184,422)(185,395)
(186,396)(187,397)(188,398)(189,399)(190,400)(191,401)(192,402)(193,403)
(194,404)(195,405)(196,406)(197,407)(198,408)(199,437)(200,438)(201,439)
(202,440)(203,441)(204,442)(205,443)(206,444)(207,445)(208,446)(209,447)
(210,448)(211,449)(212,450)(213,423)(214,424)(215,425)(216,426)(217,427)
(218,428)(219,429)(220,430)(221,431)(222,432)(223,433)(224,434)(225,435)
(226,436);
poly := sub<Sym(450)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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*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 >; 
 

to this polytope