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Polytope of Type {2,16,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16,28}*1792a
if this polytope has a name.
Group : SmallGroup(1792,323305)
Rank : 4
Schlafli Type : {2,16,28}
Number of vertices, edges, etc : 2, 16, 224, 28
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 : {2,8,28}*896a, {2,16,14}*896
   4-fold quotients : {2,4,28}*448, {2,8,14}*448
   7-fold quotients : {2,16,4}*256a
   8-fold quotients : {2,2,28}*224, {2,4,14}*224
   14-fold quotients : {2,8,4}*128a, {2,16,2}*128
   16-fold quotients : {2,2,14}*112
   28-fold quotients : {2,4,4}*64, {2,8,2}*64
   32-fold quotients : {2,2,7}*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 := (  3,227)(  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);;
s2 := (  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 17, 24)( 18, 30)
( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 32, 37)( 33, 36)( 34, 35)
( 39, 44)( 40, 43)( 41, 42)( 45, 52)( 46, 58)( 47, 57)( 48, 56)( 49, 55)
( 50, 54)( 51, 53)( 59, 73)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)
( 65, 74)( 66, 80)( 67, 86)( 68, 85)( 69, 84)( 70, 83)( 71, 82)( 72, 81)
( 87,101)( 88,107)( 89,106)( 90,105)( 91,104)( 92,103)( 93,102)( 94,108)
( 95,114)( 96,113)( 97,112)( 98,111)( 99,110)(100,109)(115,143)(116,149)
(117,148)(118,147)(119,146)(120,145)(121,144)(122,150)(123,156)(124,155)
(125,154)(126,153)(127,152)(128,151)(129,164)(130,170)(131,169)(132,168)
(133,167)(134,166)(135,165)(136,157)(137,163)(138,162)(139,161)(140,160)
(141,159)(142,158)(171,213)(172,219)(173,218)(174,217)(175,216)(176,215)
(177,214)(178,220)(179,226)(180,225)(181,224)(182,223)(183,222)(184,221)
(185,199)(186,205)(187,204)(188,203)(189,202)(190,201)(191,200)(192,206)
(193,212)(194,211)(195,210)(196,209)(197,208)(198,207)(227,283)(228,289)
(229,288)(230,287)(231,286)(232,285)(233,284)(234,290)(235,296)(236,295)
(237,294)(238,293)(239,292)(240,291)(241,304)(242,310)(243,309)(244,308)
(245,307)(246,306)(247,305)(248,297)(249,303)(250,302)(251,301)(252,300)
(253,299)(254,298)(255,311)(256,317)(257,316)(258,315)(259,314)(260,313)
(261,312)(262,318)(263,324)(264,323)(265,322)(266,321)(267,320)(268,319)
(269,332)(270,338)(271,337)(272,336)(273,335)(274,334)(275,333)(276,325)
(277,331)(278,330)(279,329)(280,328)(281,327)(282,326)(339,423)(340,429)
(341,428)(342,427)(343,426)(344,425)(345,424)(346,430)(347,436)(348,435)
(349,434)(350,433)(351,432)(352,431)(353,444)(354,450)(355,449)(356,448)
(357,447)(358,446)(359,445)(360,437)(361,443)(362,442)(363,441)(364,440)
(365,439)(366,438)(367,395)(368,401)(369,400)(370,399)(371,398)(372,397)
(373,396)(374,402)(375,408)(376,407)(377,406)(378,405)(379,404)(380,403)
(381,416)(382,422)(383,421)(384,420)(385,419)(386,418)(387,417)(388,409)
(389,415)(390,414)(391,413)(392,412)(393,411)(394,410);;
s3 := (  3,116)(  4,115)(  5,121)(  6,120)(  7,119)(  8,118)(  9,117)( 10,123)
( 11,122)( 12,128)( 13,127)( 14,126)( 15,125)( 16,124)( 17,130)( 18,129)
( 19,135)( 20,134)( 21,133)( 22,132)( 23,131)( 24,137)( 25,136)( 26,142)
( 27,141)( 28,140)( 29,139)( 30,138)( 31,144)( 32,143)( 33,149)( 34,148)
( 35,147)( 36,146)( 37,145)( 38,151)( 39,150)( 40,156)( 41,155)( 42,154)
( 43,153)( 44,152)( 45,158)( 46,157)( 47,163)( 48,162)( 49,161)( 50,160)
( 51,159)( 52,165)( 53,164)( 54,170)( 55,169)( 56,168)( 57,167)( 58,166)
( 59,172)( 60,171)( 61,177)( 62,176)( 63,175)( 64,174)( 65,173)( 66,179)
( 67,178)( 68,184)( 69,183)( 70,182)( 71,181)( 72,180)( 73,186)( 74,185)
( 75,191)( 76,190)( 77,189)( 78,188)( 79,187)( 80,193)( 81,192)( 82,198)
( 83,197)( 84,196)( 85,195)( 86,194)( 87,200)( 88,199)( 89,205)( 90,204)
( 91,203)( 92,202)( 93,201)( 94,207)( 95,206)( 96,212)( 97,211)( 98,210)
( 99,209)(100,208)(101,214)(102,213)(103,219)(104,218)(105,217)(106,216)
(107,215)(108,221)(109,220)(110,226)(111,225)(112,224)(113,223)(114,222)
(227,340)(228,339)(229,345)(230,344)(231,343)(232,342)(233,341)(234,347)
(235,346)(236,352)(237,351)(238,350)(239,349)(240,348)(241,354)(242,353)
(243,359)(244,358)(245,357)(246,356)(247,355)(248,361)(249,360)(250,366)
(251,365)(252,364)(253,363)(254,362)(255,368)(256,367)(257,373)(258,372)
(259,371)(260,370)(261,369)(262,375)(263,374)(264,380)(265,379)(266,378)
(267,377)(268,376)(269,382)(270,381)(271,387)(272,386)(273,385)(274,384)
(275,383)(276,389)(277,388)(278,394)(279,393)(280,392)(281,391)(282,390)
(283,396)(284,395)(285,401)(286,400)(287,399)(288,398)(289,397)(290,403)
(291,402)(292,408)(293,407)(294,406)(295,405)(296,404)(297,410)(298,409)
(299,415)(300,414)(301,413)(302,412)(303,411)(304,417)(305,416)(306,422)
(307,421)(308,420)(309,419)(310,418)(311,424)(312,423)(313,429)(314,428)
(315,427)(316,426)(317,425)(318,431)(319,430)(320,436)(321,435)(322,434)
(323,433)(324,432)(325,438)(326,437)(327,443)(328,442)(329,441)(330,440)
(331,439)(332,445)(333,444)(334,450)(335,449)(336,448)(337,447)(338,446);;
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, 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, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(450)!(1,2);
s1 := 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);
s2 := Sym(450)!(  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 17, 24)
( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)( 23, 25)( 32, 37)( 33, 36)
( 34, 35)( 39, 44)( 40, 43)( 41, 42)( 45, 52)( 46, 58)( 47, 57)( 48, 56)
( 49, 55)( 50, 54)( 51, 53)( 59, 73)( 60, 79)( 61, 78)( 62, 77)( 63, 76)
( 64, 75)( 65, 74)( 66, 80)( 67, 86)( 68, 85)( 69, 84)( 70, 83)( 71, 82)
( 72, 81)( 87,101)( 88,107)( 89,106)( 90,105)( 91,104)( 92,103)( 93,102)
( 94,108)( 95,114)( 96,113)( 97,112)( 98,111)( 99,110)(100,109)(115,143)
(116,149)(117,148)(118,147)(119,146)(120,145)(121,144)(122,150)(123,156)
(124,155)(125,154)(126,153)(127,152)(128,151)(129,164)(130,170)(131,169)
(132,168)(133,167)(134,166)(135,165)(136,157)(137,163)(138,162)(139,161)
(140,160)(141,159)(142,158)(171,213)(172,219)(173,218)(174,217)(175,216)
(176,215)(177,214)(178,220)(179,226)(180,225)(181,224)(182,223)(183,222)
(184,221)(185,199)(186,205)(187,204)(188,203)(189,202)(190,201)(191,200)
(192,206)(193,212)(194,211)(195,210)(196,209)(197,208)(198,207)(227,283)
(228,289)(229,288)(230,287)(231,286)(232,285)(233,284)(234,290)(235,296)
(236,295)(237,294)(238,293)(239,292)(240,291)(241,304)(242,310)(243,309)
(244,308)(245,307)(246,306)(247,305)(248,297)(249,303)(250,302)(251,301)
(252,300)(253,299)(254,298)(255,311)(256,317)(257,316)(258,315)(259,314)
(260,313)(261,312)(262,318)(263,324)(264,323)(265,322)(266,321)(267,320)
(268,319)(269,332)(270,338)(271,337)(272,336)(273,335)(274,334)(275,333)
(276,325)(277,331)(278,330)(279,329)(280,328)(281,327)(282,326)(339,423)
(340,429)(341,428)(342,427)(343,426)(344,425)(345,424)(346,430)(347,436)
(348,435)(349,434)(350,433)(351,432)(352,431)(353,444)(354,450)(355,449)
(356,448)(357,447)(358,446)(359,445)(360,437)(361,443)(362,442)(363,441)
(364,440)(365,439)(366,438)(367,395)(368,401)(369,400)(370,399)(371,398)
(372,397)(373,396)(374,402)(375,408)(376,407)(377,406)(378,405)(379,404)
(380,403)(381,416)(382,422)(383,421)(384,420)(385,419)(386,418)(387,417)
(388,409)(389,415)(390,414)(391,413)(392,412)(393,411)(394,410);
s3 := Sym(450)!(  3,116)(  4,115)(  5,121)(  6,120)(  7,119)(  8,118)(  9,117)
( 10,123)( 11,122)( 12,128)( 13,127)( 14,126)( 15,125)( 16,124)( 17,130)
( 18,129)( 19,135)( 20,134)( 21,133)( 22,132)( 23,131)( 24,137)( 25,136)
( 26,142)( 27,141)( 28,140)( 29,139)( 30,138)( 31,144)( 32,143)( 33,149)
( 34,148)( 35,147)( 36,146)( 37,145)( 38,151)( 39,150)( 40,156)( 41,155)
( 42,154)( 43,153)( 44,152)( 45,158)( 46,157)( 47,163)( 48,162)( 49,161)
( 50,160)( 51,159)( 52,165)( 53,164)( 54,170)( 55,169)( 56,168)( 57,167)
( 58,166)( 59,172)( 60,171)( 61,177)( 62,176)( 63,175)( 64,174)( 65,173)
( 66,179)( 67,178)( 68,184)( 69,183)( 70,182)( 71,181)( 72,180)( 73,186)
( 74,185)( 75,191)( 76,190)( 77,189)( 78,188)( 79,187)( 80,193)( 81,192)
( 82,198)( 83,197)( 84,196)( 85,195)( 86,194)( 87,200)( 88,199)( 89,205)
( 90,204)( 91,203)( 92,202)( 93,201)( 94,207)( 95,206)( 96,212)( 97,211)
( 98,210)( 99,209)(100,208)(101,214)(102,213)(103,219)(104,218)(105,217)
(106,216)(107,215)(108,221)(109,220)(110,226)(111,225)(112,224)(113,223)
(114,222)(227,340)(228,339)(229,345)(230,344)(231,343)(232,342)(233,341)
(234,347)(235,346)(236,352)(237,351)(238,350)(239,349)(240,348)(241,354)
(242,353)(243,359)(244,358)(245,357)(246,356)(247,355)(248,361)(249,360)
(250,366)(251,365)(252,364)(253,363)(254,362)(255,368)(256,367)(257,373)
(258,372)(259,371)(260,370)(261,369)(262,375)(263,374)(264,380)(265,379)
(266,378)(267,377)(268,376)(269,382)(270,381)(271,387)(272,386)(273,385)
(274,384)(275,383)(276,389)(277,388)(278,394)(279,393)(280,392)(281,391)
(282,390)(283,396)(284,395)(285,401)(286,400)(287,399)(288,398)(289,397)
(290,403)(291,402)(292,408)(293,407)(294,406)(295,405)(296,404)(297,410)
(298,409)(299,415)(300,414)(301,413)(302,412)(303,411)(304,417)(305,416)
(306,422)(307,421)(308,420)(309,419)(310,418)(311,424)(312,423)(313,429)
(314,428)(315,427)(316,426)(317,425)(318,431)(319,430)(320,436)(321,435)
(322,434)(323,433)(324,432)(325,438)(326,437)(327,443)(328,442)(329,441)
(330,440)(331,439)(332,445)(333,444)(334,450)(335,449)(336,448)(337,447)
(338,446);
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, 
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, 
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

to this polytope