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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}*1792b
if this polytope has a name.
Group : SmallGroup(1792,323453)
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
   4-fold quotients : {2,4,28}*448, {2,8,14}*448
   7-fold quotients : {2,16,4}*256b
   8-fold quotients : {2,2,28}*224, {2,4,14}*224
   14-fold quotients : {2,8,4}*128a
   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)( 31,262)( 32,263)( 33,264)( 34,265)
( 35,266)( 36,267)( 37,268)( 38,255)( 39,256)( 40,257)( 41,258)( 42,259)
( 43,260)( 44,261)( 45,269)( 46,270)( 47,271)( 48,272)( 49,273)( 50,274)
( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)( 57,281)( 58,282)
( 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)( 87,332)( 88,333)( 89,334)( 90,335)
( 91,336)( 92,337)( 93,338)( 94,325)( 95,326)( 96,327)( 97,328)( 98,329)
( 99,330)(100,331)(101,318)(102,319)(103,320)(104,321)(105,322)(106,323)
(107,324)(108,311)(109,312)(110,313)(111,314)(112,315)(113,316)(114,317)
(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)(143,374)(144,375)(145,376)(146,377)
(147,378)(148,379)(149,380)(150,367)(151,368)(152,369)(153,370)(154,371)
(155,372)(156,373)(157,381)(158,382)(159,383)(160,384)(161,385)(162,386)
(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)(169,393)(170,394)
(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)(199,444)(200,445)(201,446)(202,447)
(203,448)(204,449)(205,450)(206,437)(207,438)(208,439)(209,440)(210,441)
(211,442)(212,443)(213,430)(214,431)(215,432)(216,433)(217,434)(218,435)
(219,436)(220,423)(221,424)(222,425)(223,426)(224,427)(225,428)(226,429);;
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)(339,430)(340,436)
(341,435)(342,434)(343,433)(344,432)(345,431)(346,423)(347,429)(348,428)
(349,427)(350,426)(351,425)(352,424)(353,437)(354,443)(355,442)(356,441)
(357,440)(358,439)(359,438)(360,444)(361,450)(362,449)(363,448)(364,447)
(365,446)(366,445)(367,402)(368,408)(369,407)(370,406)(371,405)(372,404)
(373,403)(374,395)(375,401)(376,400)(377,399)(378,398)(379,397)(380,396)
(381,409)(382,415)(383,414)(384,413)(385,412)(386,411)(387,410)(388,416)
(389,422)(390,421)(391,420)(392,419)(393,418)(394,417);;
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)
( 59,179)( 60,178)( 61,184)( 62,183)( 63,182)( 64,181)( 65,180)( 66,172)
( 67,171)( 68,177)( 69,176)( 70,175)( 71,174)( 72,173)( 73,193)( 74,192)
( 75,198)( 76,197)( 77,196)( 78,195)( 79,194)( 80,186)( 81,185)( 82,191)
( 83,190)( 84,189)( 85,188)( 86,187)( 87,207)( 88,206)( 89,212)( 90,211)
( 91,210)( 92,209)( 93,208)( 94,200)( 95,199)( 96,205)( 97,204)( 98,203)
( 99,202)(100,201)(101,221)(102,220)(103,226)(104,225)(105,224)(106,223)
(107,222)(108,214)(109,213)(110,219)(111,218)(112,217)(113,216)(114,215)
(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)
(283,403)(284,402)(285,408)(286,407)(287,406)(288,405)(289,404)(290,396)
(291,395)(292,401)(293,400)(294,399)(295,398)(296,397)(297,417)(298,416)
(299,422)(300,421)(301,420)(302,419)(303,418)(304,410)(305,409)(306,415)
(307,414)(308,413)(309,412)(310,411)(311,431)(312,430)(313,436)(314,435)
(315,434)(316,433)(317,432)(318,424)(319,423)(320,429)(321,428)(322,427)
(323,426)(324,425)(325,445)(326,444)(327,450)(328,449)(329,448)(330,447)
(331,446)(332,438)(333,437)(334,443)(335,442)(336,441)(337,440)(338,439);;
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, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*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*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)( 31,262)( 32,263)( 33,264)
( 34,265)( 35,266)( 36,267)( 37,268)( 38,255)( 39,256)( 40,257)( 41,258)
( 42,259)( 43,260)( 44,261)( 45,269)( 46,270)( 47,271)( 48,272)( 49,273)
( 50,274)( 51,275)( 52,276)( 53,277)( 54,278)( 55,279)( 56,280)( 57,281)
( 58,282)( 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)( 87,332)( 88,333)( 89,334)
( 90,335)( 91,336)( 92,337)( 93,338)( 94,325)( 95,326)( 96,327)( 97,328)
( 98,329)( 99,330)(100,331)(101,318)(102,319)(103,320)(104,321)(105,322)
(106,323)(107,324)(108,311)(109,312)(110,313)(111,314)(112,315)(113,316)
(114,317)(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)(143,374)(144,375)(145,376)
(146,377)(147,378)(148,379)(149,380)(150,367)(151,368)(152,369)(153,370)
(154,371)(155,372)(156,373)(157,381)(158,382)(159,383)(160,384)(161,385)
(162,386)(163,387)(164,388)(165,389)(166,390)(167,391)(168,392)(169,393)
(170,394)(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)(199,444)(200,445)(201,446)
(202,447)(203,448)(204,449)(205,450)(206,437)(207,438)(208,439)(209,440)
(210,441)(211,442)(212,443)(213,430)(214,431)(215,432)(216,433)(217,434)
(218,435)(219,436)(220,423)(221,424)(222,425)(223,426)(224,427)(225,428)
(226,429);
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)(339,430)
(340,436)(341,435)(342,434)(343,433)(344,432)(345,431)(346,423)(347,429)
(348,428)(349,427)(350,426)(351,425)(352,424)(353,437)(354,443)(355,442)
(356,441)(357,440)(358,439)(359,438)(360,444)(361,450)(362,449)(363,448)
(364,447)(365,446)(366,445)(367,402)(368,408)(369,407)(370,406)(371,405)
(372,404)(373,403)(374,395)(375,401)(376,400)(377,399)(378,398)(379,397)
(380,396)(381,409)(382,415)(383,414)(384,413)(385,412)(386,411)(387,410)
(388,416)(389,422)(390,421)(391,420)(392,419)(393,418)(394,417);
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)( 59,179)( 60,178)( 61,184)( 62,183)( 63,182)( 64,181)( 65,180)
( 66,172)( 67,171)( 68,177)( 69,176)( 70,175)( 71,174)( 72,173)( 73,193)
( 74,192)( 75,198)( 76,197)( 77,196)( 78,195)( 79,194)( 80,186)( 81,185)
( 82,191)( 83,190)( 84,189)( 85,188)( 86,187)( 87,207)( 88,206)( 89,212)
( 90,211)( 91,210)( 92,209)( 93,208)( 94,200)( 95,199)( 96,205)( 97,204)
( 98,203)( 99,202)(100,201)(101,221)(102,220)(103,226)(104,225)(105,224)
(106,223)(107,222)(108,214)(109,213)(110,219)(111,218)(112,217)(113,216)
(114,215)(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)(283,403)(284,402)(285,408)(286,407)(287,406)(288,405)(289,404)
(290,396)(291,395)(292,401)(293,400)(294,399)(295,398)(296,397)(297,417)
(298,416)(299,422)(300,421)(301,420)(302,419)(303,418)(304,410)(305,409)
(306,415)(307,414)(308,413)(309,412)(310,411)(311,431)(312,430)(313,436)
(314,435)(315,434)(316,433)(317,432)(318,424)(319,423)(320,429)(321,428)
(322,427)(323,426)(324,425)(325,445)(326,444)(327,450)(328,449)(329,448)
(330,447)(331,446)(332,438)(333,437)(334,443)(335,442)(336,441)(337,440)
(338,439);
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, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*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*s2*s3 >; 
 

to this polytope