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Polytope of Type {32,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {32,14}*896
Also Known As : {32,14|2}. if this polytope has another name.
Group : SmallGroup(896,1895)
Rank : 3
Schlafli Type : {32,14}
Number of vertices, edges, etc : 32, 224, 14
Order of s0s1s2 : 224
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {32,14,2} of size 1792
Vertex Figure Of :
   {2,32,14} of size 1792
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {16,14}*448
   4-fold quotients : {8,14}*224
   7-fold quotients : {32,2}*128
   8-fold quotients : {4,14}*112
   14-fold quotients : {16,2}*64
   16-fold quotients : {2,14}*56
   28-fold quotients : {8,2}*32
   32-fold quotients : {2,7}*28
   56-fold quotients : {4,2}*16
   112-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {32,28}*1792a, {64,14}*1792
Permutation Representation (GAP) :
s0 := ( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 29, 43)
( 30, 44)( 31, 45)( 32, 46)( 33, 47)( 34, 48)( 35, 49)( 36, 50)( 37, 51)
( 38, 52)( 39, 53)( 40, 54)( 41, 55)( 42, 56)( 57, 85)( 58, 86)( 59, 87)
( 60, 88)( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)( 67, 95)
( 68, 96)( 69, 97)( 70, 98)( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)
( 76,111)( 77,112)( 78, 99)( 79,100)( 80,101)( 81,102)( 82,103)( 83,104)
( 84,105)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)(133,140)
(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)
(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(169,197)(170,198)
(171,199)(172,200)(173,201)(174,202)(175,203)(176,204)(177,205)(178,206)
(179,207)(180,208)(181,209)(182,210)(183,218)(184,219)(185,220)(186,221)
(187,222)(188,223)(189,224)(190,211)(191,212)(192,213)(193,214)(194,215)
(195,216)(196,217)(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)
(239,302)(240,303)(241,304)(242,305)(243,306)(244,307)(245,308)(246,295)
(247,296)(248,297)(249,298)(250,299)(251,300)(252,301)(253,323)(254,324)
(255,325)(256,326)(257,327)(258,328)(259,329)(260,330)(261,331)(262,332)
(263,333)(264,334)(265,335)(266,336)(267,309)(268,310)(269,311)(270,312)
(271,313)(272,314)(273,315)(274,316)(275,317)(276,318)(277,319)(278,320)
(279,321)(280,322)(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)
(351,414)(352,415)(353,416)(354,417)(355,418)(356,419)(357,420)(358,407)
(359,408)(360,409)(361,410)(362,411)(363,412)(364,413)(365,435)(366,436)
(367,437)(368,438)(369,439)(370,440)(371,441)(372,442)(373,443)(374,444)
(375,445)(376,446)(377,447)(378,448)(379,421)(380,422)(381,423)(382,424)
(383,425)(384,426)(385,427)(386,428)(387,429)(388,430)(389,431)(390,432)
(391,433)(392,434);;
s1 := (  1,337)(  2,343)(  3,342)(  4,341)(  5,340)(  6,339)(  7,338)(  8,344)
(  9,350)( 10,349)( 11,348)( 12,347)( 13,346)( 14,345)( 15,358)( 16,364)
( 17,363)( 18,362)( 19,361)( 20,360)( 21,359)( 22,351)( 23,357)( 24,356)
( 25,355)( 26,354)( 27,353)( 28,352)( 29,379)( 30,385)( 31,384)( 32,383)
( 33,382)( 34,381)( 35,380)( 36,386)( 37,392)( 38,391)( 39,390)( 40,389)
( 41,388)( 42,387)( 43,365)( 44,371)( 45,370)( 46,369)( 47,368)( 48,367)
( 49,366)( 50,372)( 51,378)( 52,377)( 53,376)( 54,375)( 55,374)( 56,373)
( 57,421)( 58,427)( 59,426)( 60,425)( 61,424)( 62,423)( 63,422)( 64,428)
( 65,434)( 66,433)( 67,432)( 68,431)( 69,430)( 70,429)( 71,442)( 72,448)
( 73,447)( 74,446)( 75,445)( 76,444)( 77,443)( 78,435)( 79,441)( 80,440)
( 81,439)( 82,438)( 83,437)( 84,436)( 85,393)( 86,399)( 87,398)( 88,397)
( 89,396)( 90,395)( 91,394)( 92,400)( 93,406)( 94,405)( 95,404)( 96,403)
( 97,402)( 98,401)( 99,414)(100,420)(101,419)(102,418)(103,417)(104,416)
(105,415)(106,407)(107,413)(108,412)(109,411)(110,410)(111,409)(112,408)
(113,225)(114,231)(115,230)(116,229)(117,228)(118,227)(119,226)(120,232)
(121,238)(122,237)(123,236)(124,235)(125,234)(126,233)(127,246)(128,252)
(129,251)(130,250)(131,249)(132,248)(133,247)(134,239)(135,245)(136,244)
(137,243)(138,242)(139,241)(140,240)(141,267)(142,273)(143,272)(144,271)
(145,270)(146,269)(147,268)(148,274)(149,280)(150,279)(151,278)(152,277)
(153,276)(154,275)(155,253)(156,259)(157,258)(158,257)(159,256)(160,255)
(161,254)(162,260)(163,266)(164,265)(165,264)(166,263)(167,262)(168,261)
(169,309)(170,315)(171,314)(172,313)(173,312)(174,311)(175,310)(176,316)
(177,322)(178,321)(179,320)(180,319)(181,318)(182,317)(183,330)(184,336)
(185,335)(186,334)(187,333)(188,332)(189,331)(190,323)(191,329)(192,328)
(193,327)(194,326)(195,325)(196,324)(197,281)(198,287)(199,286)(200,285)
(201,284)(202,283)(203,282)(204,288)(205,294)(206,293)(207,292)(208,291)
(209,290)(210,289)(211,302)(212,308)(213,307)(214,306)(215,305)(216,304)
(217,303)(218,295)(219,301)(220,300)(221,299)(222,298)(223,297)(224,296);;
s2 := (  1,114)(  2,113)(  3,119)(  4,118)(  5,117)(  6,116)(  7,115)(  8,121)
(  9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,128)( 16,127)
( 17,133)( 18,132)( 19,131)( 20,130)( 21,129)( 22,135)( 23,134)( 24,140)
( 25,139)( 26,138)( 27,137)( 28,136)( 29,142)( 30,141)( 31,147)( 32,146)
( 33,145)( 34,144)( 35,143)( 36,149)( 37,148)( 38,154)( 39,153)( 40,152)
( 41,151)( 42,150)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)( 48,158)
( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)
( 57,170)( 58,169)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)( 64,177)
( 65,176)( 66,182)( 67,181)( 68,180)( 69,179)( 70,178)( 71,184)( 72,183)
( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,191)( 79,190)( 80,196)
( 81,195)( 82,194)( 83,193)( 84,192)( 85,198)( 86,197)( 87,203)( 88,202)
( 89,201)( 90,200)( 91,199)( 92,205)( 93,204)( 94,210)( 95,209)( 96,208)
( 97,207)( 98,206)( 99,212)(100,211)(101,217)(102,216)(103,215)(104,214)
(105,213)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)(112,220)
(225,338)(226,337)(227,343)(228,342)(229,341)(230,340)(231,339)(232,345)
(233,344)(234,350)(235,349)(236,348)(237,347)(238,346)(239,352)(240,351)
(241,357)(242,356)(243,355)(244,354)(245,353)(246,359)(247,358)(248,364)
(249,363)(250,362)(251,361)(252,360)(253,366)(254,365)(255,371)(256,370)
(257,369)(258,368)(259,367)(260,373)(261,372)(262,378)(263,377)(264,376)
(265,375)(266,374)(267,380)(268,379)(269,385)(270,384)(271,383)(272,382)
(273,381)(274,387)(275,386)(276,392)(277,391)(278,390)(279,389)(280,388)
(281,394)(282,393)(283,399)(284,398)(285,397)(286,396)(287,395)(288,401)
(289,400)(290,406)(291,405)(292,404)(293,403)(294,402)(295,408)(296,407)
(297,413)(298,412)(299,411)(300,410)(301,409)(302,415)(303,414)(304,420)
(305,419)(306,418)(307,417)(308,416)(309,422)(310,421)(311,427)(312,426)
(313,425)(314,424)(315,423)(316,429)(317,428)(318,434)(319,433)(320,432)
(321,431)(322,430)(323,436)(324,435)(325,441)(326,440)(327,439)(328,438)
(329,437)(330,443)(331,442)(332,448)(333,447)(334,446)(335,445)(336,444);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(448)!( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)
( 29, 43)( 30, 44)( 31, 45)( 32, 46)( 33, 47)( 34, 48)( 35, 49)( 36, 50)
( 37, 51)( 38, 52)( 39, 53)( 40, 54)( 41, 55)( 42, 56)( 57, 85)( 58, 86)
( 59, 87)( 60, 88)( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)
( 67, 95)( 68, 96)( 69, 97)( 70, 98)( 71,106)( 72,107)( 73,108)( 74,109)
( 75,110)( 76,111)( 77,112)( 78, 99)( 79,100)( 80,101)( 81,102)( 82,103)
( 83,104)( 84,105)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)
(133,140)(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161)
(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(169,197)
(170,198)(171,199)(172,200)(173,201)(174,202)(175,203)(176,204)(177,205)
(178,206)(179,207)(180,208)(181,209)(182,210)(183,218)(184,219)(185,220)
(186,221)(187,222)(188,223)(189,224)(190,211)(191,212)(192,213)(193,214)
(194,215)(195,216)(196,217)(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)(239,302)(240,303)(241,304)(242,305)(243,306)(244,307)(245,308)
(246,295)(247,296)(248,297)(249,298)(250,299)(251,300)(252,301)(253,323)
(254,324)(255,325)(256,326)(257,327)(258,328)(259,329)(260,330)(261,331)
(262,332)(263,333)(264,334)(265,335)(266,336)(267,309)(268,310)(269,311)
(270,312)(271,313)(272,314)(273,315)(274,316)(275,317)(276,318)(277,319)
(278,320)(279,321)(280,322)(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)(351,414)(352,415)(353,416)(354,417)(355,418)(356,419)(357,420)
(358,407)(359,408)(360,409)(361,410)(362,411)(363,412)(364,413)(365,435)
(366,436)(367,437)(368,438)(369,439)(370,440)(371,441)(372,442)(373,443)
(374,444)(375,445)(376,446)(377,447)(378,448)(379,421)(380,422)(381,423)
(382,424)(383,425)(384,426)(385,427)(386,428)(387,429)(388,430)(389,431)
(390,432)(391,433)(392,434);
s1 := Sym(448)!(  1,337)(  2,343)(  3,342)(  4,341)(  5,340)(  6,339)(  7,338)
(  8,344)(  9,350)( 10,349)( 11,348)( 12,347)( 13,346)( 14,345)( 15,358)
( 16,364)( 17,363)( 18,362)( 19,361)( 20,360)( 21,359)( 22,351)( 23,357)
( 24,356)( 25,355)( 26,354)( 27,353)( 28,352)( 29,379)( 30,385)( 31,384)
( 32,383)( 33,382)( 34,381)( 35,380)( 36,386)( 37,392)( 38,391)( 39,390)
( 40,389)( 41,388)( 42,387)( 43,365)( 44,371)( 45,370)( 46,369)( 47,368)
( 48,367)( 49,366)( 50,372)( 51,378)( 52,377)( 53,376)( 54,375)( 55,374)
( 56,373)( 57,421)( 58,427)( 59,426)( 60,425)( 61,424)( 62,423)( 63,422)
( 64,428)( 65,434)( 66,433)( 67,432)( 68,431)( 69,430)( 70,429)( 71,442)
( 72,448)( 73,447)( 74,446)( 75,445)( 76,444)( 77,443)( 78,435)( 79,441)
( 80,440)( 81,439)( 82,438)( 83,437)( 84,436)( 85,393)( 86,399)( 87,398)
( 88,397)( 89,396)( 90,395)( 91,394)( 92,400)( 93,406)( 94,405)( 95,404)
( 96,403)( 97,402)( 98,401)( 99,414)(100,420)(101,419)(102,418)(103,417)
(104,416)(105,415)(106,407)(107,413)(108,412)(109,411)(110,410)(111,409)
(112,408)(113,225)(114,231)(115,230)(116,229)(117,228)(118,227)(119,226)
(120,232)(121,238)(122,237)(123,236)(124,235)(125,234)(126,233)(127,246)
(128,252)(129,251)(130,250)(131,249)(132,248)(133,247)(134,239)(135,245)
(136,244)(137,243)(138,242)(139,241)(140,240)(141,267)(142,273)(143,272)
(144,271)(145,270)(146,269)(147,268)(148,274)(149,280)(150,279)(151,278)
(152,277)(153,276)(154,275)(155,253)(156,259)(157,258)(158,257)(159,256)
(160,255)(161,254)(162,260)(163,266)(164,265)(165,264)(166,263)(167,262)
(168,261)(169,309)(170,315)(171,314)(172,313)(173,312)(174,311)(175,310)
(176,316)(177,322)(178,321)(179,320)(180,319)(181,318)(182,317)(183,330)
(184,336)(185,335)(186,334)(187,333)(188,332)(189,331)(190,323)(191,329)
(192,328)(193,327)(194,326)(195,325)(196,324)(197,281)(198,287)(199,286)
(200,285)(201,284)(202,283)(203,282)(204,288)(205,294)(206,293)(207,292)
(208,291)(209,290)(210,289)(211,302)(212,308)(213,307)(214,306)(215,305)
(216,304)(217,303)(218,295)(219,301)(220,300)(221,299)(222,298)(223,297)
(224,296);
s2 := Sym(448)!(  1,114)(  2,113)(  3,119)(  4,118)(  5,117)(  6,116)(  7,115)
(  8,121)(  9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,128)
( 16,127)( 17,133)( 18,132)( 19,131)( 20,130)( 21,129)( 22,135)( 23,134)
( 24,140)( 25,139)( 26,138)( 27,137)( 28,136)( 29,142)( 30,141)( 31,147)
( 32,146)( 33,145)( 34,144)( 35,143)( 36,149)( 37,148)( 38,154)( 39,153)
( 40,152)( 41,151)( 42,150)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)
( 48,158)( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)
( 56,164)( 57,170)( 58,169)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)
( 64,177)( 65,176)( 66,182)( 67,181)( 68,180)( 69,179)( 70,178)( 71,184)
( 72,183)( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,191)( 79,190)
( 80,196)( 81,195)( 82,194)( 83,193)( 84,192)( 85,198)( 86,197)( 87,203)
( 88,202)( 89,201)( 90,200)( 91,199)( 92,205)( 93,204)( 94,210)( 95,209)
( 96,208)( 97,207)( 98,206)( 99,212)(100,211)(101,217)(102,216)(103,215)
(104,214)(105,213)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)
(112,220)(225,338)(226,337)(227,343)(228,342)(229,341)(230,340)(231,339)
(232,345)(233,344)(234,350)(235,349)(236,348)(237,347)(238,346)(239,352)
(240,351)(241,357)(242,356)(243,355)(244,354)(245,353)(246,359)(247,358)
(248,364)(249,363)(250,362)(251,361)(252,360)(253,366)(254,365)(255,371)
(256,370)(257,369)(258,368)(259,367)(260,373)(261,372)(262,378)(263,377)
(264,376)(265,375)(266,374)(267,380)(268,379)(269,385)(270,384)(271,383)
(272,382)(273,381)(274,387)(275,386)(276,392)(277,391)(278,390)(279,389)
(280,388)(281,394)(282,393)(283,399)(284,398)(285,397)(286,396)(287,395)
(288,401)(289,400)(290,406)(291,405)(292,404)(293,403)(294,402)(295,408)
(296,407)(297,413)(298,412)(299,411)(300,410)(301,409)(302,415)(303,414)
(304,420)(305,419)(306,418)(307,417)(308,416)(309,422)(310,421)(311,427)
(312,426)(313,425)(314,424)(315,423)(316,429)(317,428)(318,434)(319,433)
(320,432)(321,431)(322,430)(323,436)(324,435)(325,441)(326,440)(327,439)
(328,438)(329,437)(330,443)(331,442)(332,448)(333,447)(334,446)(335,445)
(336,444);
poly := sub<Sym(448)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope