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Polytope of Type {2,32,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,32,14}*1792
if this polytope has a name.
Group : SmallGroup(1792,327682)
Rank : 4
Schlafli Type : {2,32,14}
Number of vertices, edges, etc : 2, 32, 224, 14
Order of s0s1s2s3 : 224
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 : {2,16,14}*896
   4-fold quotients : {2,8,14}*448
   7-fold quotients : {2,32,2}*256
   8-fold quotients : {2,4,14}*224
   14-fold quotients : {2,16,2}*128
   16-fold quotients : {2,2,14}*112
   28-fold quotients : {2,8,2}*64
   32-fold quotients : {2,2,7}*56
   56-fold quotients : {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 := ( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 22, 29)( 23, 30)( 31, 45)
( 32, 46)( 33, 47)( 34, 48)( 35, 49)( 36, 50)( 37, 51)( 38, 52)( 39, 53)
( 40, 54)( 41, 55)( 42, 56)( 43, 57)( 44, 58)( 59, 87)( 60, 88)( 61, 89)
( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)( 67, 95)( 68, 96)( 69, 97)
( 70, 98)( 71, 99)( 72,100)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)
( 78,113)( 79,114)( 80,101)( 81,102)( 82,103)( 83,104)( 84,105)( 85,106)
( 86,107)(129,136)(130,137)(131,138)(132,139)(133,140)(134,141)(135,142)
(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)(149,163)(150,164)
(151,165)(152,166)(153,167)(154,168)(155,169)(156,170)(171,199)(172,200)
(173,201)(174,202)(175,203)(176,204)(177,205)(178,206)(179,207)(180,208)
(181,209)(182,210)(183,211)(184,212)(185,220)(186,221)(187,222)(188,223)
(189,224)(190,225)(191,226)(192,213)(193,214)(194,215)(195,216)(196,217)
(197,218)(198,219)(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)
(241,304)(242,305)(243,306)(244,307)(245,308)(246,309)(247,310)(248,297)
(249,298)(250,299)(251,300)(252,301)(253,302)(254,303)(255,325)(256,326)
(257,327)(258,328)(259,329)(260,330)(261,331)(262,332)(263,333)(264,334)
(265,335)(266,336)(267,337)(268,338)(269,311)(270,312)(271,313)(272,314)
(273,315)(274,316)(275,317)(276,318)(277,319)(278,320)(279,321)(280,322)
(281,323)(282,324)(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)
(353,416)(354,417)(355,418)(356,419)(357,420)(358,421)(359,422)(360,409)
(361,410)(362,411)(363,412)(364,413)(365,414)(366,415)(367,437)(368,438)
(369,439)(370,440)(371,441)(372,442)(373,443)(374,444)(375,445)(376,446)
(377,447)(378,448)(379,449)(380,450)(381,423)(382,424)(383,425)(384,426)
(385,427)(386,428)(387,429)(388,430)(389,431)(390,432)(391,433)(392,434)
(393,435)(394,436);;
s2 := (  3,339)(  4,345)(  5,344)(  6,343)(  7,342)(  8,341)(  9,340)( 10,346)
( 11,352)( 12,351)( 13,350)( 14,349)( 15,348)( 16,347)( 17,360)( 18,366)
( 19,365)( 20,364)( 21,363)( 22,362)( 23,361)( 24,353)( 25,359)( 26,358)
( 27,357)( 28,356)( 29,355)( 30,354)( 31,381)( 32,387)( 33,386)( 34,385)
( 35,384)( 36,383)( 37,382)( 38,388)( 39,394)( 40,393)( 41,392)( 42,391)
( 43,390)( 44,389)( 45,367)( 46,373)( 47,372)( 48,371)( 49,370)( 50,369)
( 51,368)( 52,374)( 53,380)( 54,379)( 55,378)( 56,377)( 57,376)( 58,375)
( 59,423)( 60,429)( 61,428)( 62,427)( 63,426)( 64,425)( 65,424)( 66,430)
( 67,436)( 68,435)( 69,434)( 70,433)( 71,432)( 72,431)( 73,444)( 74,450)
( 75,449)( 76,448)( 77,447)( 78,446)( 79,445)( 80,437)( 81,443)( 82,442)
( 83,441)( 84,440)( 85,439)( 86,438)( 87,395)( 88,401)( 89,400)( 90,399)
( 91,398)( 92,397)( 93,396)( 94,402)( 95,408)( 96,407)( 97,406)( 98,405)
( 99,404)(100,403)(101,416)(102,422)(103,421)(104,420)(105,419)(106,418)
(107,417)(108,409)(109,415)(110,414)(111,413)(112,412)(113,411)(114,410)
(115,227)(116,233)(117,232)(118,231)(119,230)(120,229)(121,228)(122,234)
(123,240)(124,239)(125,238)(126,237)(127,236)(128,235)(129,248)(130,254)
(131,253)(132,252)(133,251)(134,250)(135,249)(136,241)(137,247)(138,246)
(139,245)(140,244)(141,243)(142,242)(143,269)(144,275)(145,274)(146,273)
(147,272)(148,271)(149,270)(150,276)(151,282)(152,281)(153,280)(154,279)
(155,278)(156,277)(157,255)(158,261)(159,260)(160,259)(161,258)(162,257)
(163,256)(164,262)(165,268)(166,267)(167,266)(168,265)(169,264)(170,263)
(171,311)(172,317)(173,316)(174,315)(175,314)(176,313)(177,312)(178,318)
(179,324)(180,323)(181,322)(182,321)(183,320)(184,319)(185,332)(186,338)
(187,337)(188,336)(189,335)(190,334)(191,333)(192,325)(193,331)(194,330)
(195,329)(196,328)(197,327)(198,326)(199,283)(200,289)(201,288)(202,287)
(203,286)(204,285)(205,284)(206,290)(207,296)(208,295)(209,294)(210,293)
(211,292)(212,291)(213,304)(214,310)(215,309)(216,308)(217,307)(218,306)
(219,305)(220,297)(221,303)(222,302)(223,301)(224,300)(225,299)(226,298);;
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, 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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(450)!(1,2);
s1 := Sym(450)!( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 22, 29)( 23, 30)
( 31, 45)( 32, 46)( 33, 47)( 34, 48)( 35, 49)( 36, 50)( 37, 51)( 38, 52)
( 39, 53)( 40, 54)( 41, 55)( 42, 56)( 43, 57)( 44, 58)( 59, 87)( 60, 88)
( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)( 67, 95)( 68, 96)
( 69, 97)( 70, 98)( 71, 99)( 72,100)( 73,108)( 74,109)( 75,110)( 76,111)
( 77,112)( 78,113)( 79,114)( 80,101)( 81,102)( 82,103)( 83,104)( 84,105)
( 85,106)( 86,107)(129,136)(130,137)(131,138)(132,139)(133,140)(134,141)
(135,142)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)(149,163)
(150,164)(151,165)(152,166)(153,167)(154,168)(155,169)(156,170)(171,199)
(172,200)(173,201)(174,202)(175,203)(176,204)(177,205)(178,206)(179,207)
(180,208)(181,209)(182,210)(183,211)(184,212)(185,220)(186,221)(187,222)
(188,223)(189,224)(190,225)(191,226)(192,213)(193,214)(194,215)(195,216)
(196,217)(197,218)(198,219)(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)(241,304)(242,305)(243,306)(244,307)(245,308)(246,309)(247,310)
(248,297)(249,298)(250,299)(251,300)(252,301)(253,302)(254,303)(255,325)
(256,326)(257,327)(258,328)(259,329)(260,330)(261,331)(262,332)(263,333)
(264,334)(265,335)(266,336)(267,337)(268,338)(269,311)(270,312)(271,313)
(272,314)(273,315)(274,316)(275,317)(276,318)(277,319)(278,320)(279,321)
(280,322)(281,323)(282,324)(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)(353,416)(354,417)(355,418)(356,419)(357,420)(358,421)(359,422)
(360,409)(361,410)(362,411)(363,412)(364,413)(365,414)(366,415)(367,437)
(368,438)(369,439)(370,440)(371,441)(372,442)(373,443)(374,444)(375,445)
(376,446)(377,447)(378,448)(379,449)(380,450)(381,423)(382,424)(383,425)
(384,426)(385,427)(386,428)(387,429)(388,430)(389,431)(390,432)(391,433)
(392,434)(393,435)(394,436);
s2 := Sym(450)!(  3,339)(  4,345)(  5,344)(  6,343)(  7,342)(  8,341)(  9,340)
( 10,346)( 11,352)( 12,351)( 13,350)( 14,349)( 15,348)( 16,347)( 17,360)
( 18,366)( 19,365)( 20,364)( 21,363)( 22,362)( 23,361)( 24,353)( 25,359)
( 26,358)( 27,357)( 28,356)( 29,355)( 30,354)( 31,381)( 32,387)( 33,386)
( 34,385)( 35,384)( 36,383)( 37,382)( 38,388)( 39,394)( 40,393)( 41,392)
( 42,391)( 43,390)( 44,389)( 45,367)( 46,373)( 47,372)( 48,371)( 49,370)
( 50,369)( 51,368)( 52,374)( 53,380)( 54,379)( 55,378)( 56,377)( 57,376)
( 58,375)( 59,423)( 60,429)( 61,428)( 62,427)( 63,426)( 64,425)( 65,424)
( 66,430)( 67,436)( 68,435)( 69,434)( 70,433)( 71,432)( 72,431)( 73,444)
( 74,450)( 75,449)( 76,448)( 77,447)( 78,446)( 79,445)( 80,437)( 81,443)
( 82,442)( 83,441)( 84,440)( 85,439)( 86,438)( 87,395)( 88,401)( 89,400)
( 90,399)( 91,398)( 92,397)( 93,396)( 94,402)( 95,408)( 96,407)( 97,406)
( 98,405)( 99,404)(100,403)(101,416)(102,422)(103,421)(104,420)(105,419)
(106,418)(107,417)(108,409)(109,415)(110,414)(111,413)(112,412)(113,411)
(114,410)(115,227)(116,233)(117,232)(118,231)(119,230)(120,229)(121,228)
(122,234)(123,240)(124,239)(125,238)(126,237)(127,236)(128,235)(129,248)
(130,254)(131,253)(132,252)(133,251)(134,250)(135,249)(136,241)(137,247)
(138,246)(139,245)(140,244)(141,243)(142,242)(143,269)(144,275)(145,274)
(146,273)(147,272)(148,271)(149,270)(150,276)(151,282)(152,281)(153,280)
(154,279)(155,278)(156,277)(157,255)(158,261)(159,260)(160,259)(161,258)
(162,257)(163,256)(164,262)(165,268)(166,267)(167,266)(168,265)(169,264)
(170,263)(171,311)(172,317)(173,316)(174,315)(175,314)(176,313)(177,312)
(178,318)(179,324)(180,323)(181,322)(182,321)(183,320)(184,319)(185,332)
(186,338)(187,337)(188,336)(189,335)(190,334)(191,333)(192,325)(193,331)
(194,330)(195,329)(196,328)(197,327)(198,326)(199,283)(200,289)(201,288)
(202,287)(203,286)(204,285)(205,284)(206,290)(207,296)(208,295)(209,294)
(210,293)(211,292)(212,291)(213,304)(214,310)(215,309)(216,308)(217,307)
(218,306)(219,305)(220,297)(221,303)(222,302)(223,301)(224,300)(225,299)
(226,298);
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, 
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*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

to this polytope