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Polytope of Type {14,32,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,32,2}*1792
if this polytope has a name.
Group : SmallGroup(1792,327682)
Rank : 4
Schlafli Type : {14,32,2}
Number of vertices, edges, etc : 14, 224, 32, 2
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 : {14,16,2}*896
   4-fold quotients : {14,8,2}*448
   7-fold quotients : {2,32,2}*256
   8-fold quotients : {14,4,2}*224
   14-fold quotients : {2,16,2}*128
   16-fold quotients : {14,2,2}*112
   28-fold quotients : {2,8,2}*64
   32-fold quotients : {7,2,2}*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 := (  1,113)(  2,119)(  3,118)(  4,117)(  5,116)(  6,115)(  7,114)(  8,120)
(  9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,127)( 16,133)
( 17,132)( 18,131)( 19,130)( 20,129)( 21,128)( 22,134)( 23,140)( 24,139)
( 25,138)( 26,137)( 27,136)( 28,135)( 29,141)( 30,147)( 31,146)( 32,145)
( 33,144)( 34,143)( 35,142)( 36,148)( 37,154)( 38,153)( 39,152)( 40,151)
( 41,150)( 42,149)( 43,155)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)
( 49,156)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)
( 57,169)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)( 64,176)
( 65,182)( 66,181)( 67,180)( 68,179)( 69,178)( 70,177)( 71,183)( 72,189)
( 73,188)( 74,187)( 75,186)( 76,185)( 77,184)( 78,190)( 79,196)( 80,195)
( 81,194)( 82,193)( 83,192)( 84,191)( 85,197)( 86,203)( 87,202)( 88,201)
( 89,200)( 90,199)( 91,198)( 92,204)( 93,210)( 94,209)( 95,208)( 96,207)
( 97,206)( 98,205)( 99,211)(100,217)(101,216)(102,215)(103,214)(104,213)
(105,212)(106,218)(107,224)(108,223)(109,222)(110,221)(111,220)(112,219)
(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,344)
(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,351)(240,357)
(241,356)(242,355)(243,354)(244,353)(245,352)(246,358)(247,364)(248,363)
(249,362)(250,361)(251,360)(252,359)(253,365)(254,371)(255,370)(256,369)
(257,368)(258,367)(259,366)(260,372)(261,378)(262,377)(263,376)(264,375)
(265,374)(266,373)(267,379)(268,385)(269,384)(270,383)(271,382)(272,381)
(273,380)(274,386)(275,392)(276,391)(277,390)(278,389)(279,388)(280,387)
(281,393)(282,399)(283,398)(284,397)(285,396)(286,395)(287,394)(288,400)
(289,406)(290,405)(291,404)(292,403)(293,402)(294,401)(295,407)(296,413)
(297,412)(298,411)(299,410)(300,409)(301,408)(302,414)(303,420)(304,419)
(305,418)(306,417)(307,416)(308,415)(309,421)(310,427)(311,426)(312,425)
(313,424)(314,423)(315,422)(316,428)(317,434)(318,433)(319,432)(320,431)
(321,430)(322,429)(323,435)(324,441)(325,440)(326,439)(327,438)(328,437)
(329,436)(330,442)(331,448)(332,447)(333,446)(334,445)(335,444)(336,443);;
s1 := (  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)( 15,135)( 16,134)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,136)( 22,128)( 23,127)( 24,133)
( 25,132)( 26,131)( 27,130)( 28,129)( 29,156)( 30,155)( 31,161)( 32,160)
( 33,159)( 34,158)( 35,157)( 36,163)( 37,162)( 38,168)( 39,167)( 40,166)
( 41,165)( 42,164)( 43,142)( 44,141)( 45,147)( 46,146)( 47,145)( 48,144)
( 49,143)( 50,149)( 51,148)( 52,154)( 53,153)( 54,152)( 55,151)( 56,150)
( 57,198)( 58,197)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)( 64,205)
( 65,204)( 66,210)( 67,209)( 68,208)( 69,207)( 70,206)( 71,219)( 72,218)
( 73,224)( 74,223)( 75,222)( 76,221)( 77,220)( 78,212)( 79,211)( 80,217)
( 81,216)( 82,215)( 83,214)( 84,213)( 85,170)( 86,169)( 87,175)( 88,174)
( 89,173)( 90,172)( 91,171)( 92,177)( 93,176)( 94,182)( 95,181)( 96,180)
( 97,179)( 98,178)( 99,191)(100,190)(101,196)(102,195)(103,194)(104,193)
(105,192)(106,184)(107,183)(108,189)(109,188)(110,187)(111,186)(112,185)
(225,394)(226,393)(227,399)(228,398)(229,397)(230,396)(231,395)(232,401)
(233,400)(234,406)(235,405)(236,404)(237,403)(238,402)(239,415)(240,414)
(241,420)(242,419)(243,418)(244,417)(245,416)(246,408)(247,407)(248,413)
(249,412)(250,411)(251,410)(252,409)(253,436)(254,435)(255,441)(256,440)
(257,439)(258,438)(259,437)(260,443)(261,442)(262,448)(263,447)(264,446)
(265,445)(266,444)(267,422)(268,421)(269,427)(270,426)(271,425)(272,424)
(273,423)(274,429)(275,428)(276,434)(277,433)(278,432)(279,431)(280,430)
(281,338)(282,337)(283,343)(284,342)(285,341)(286,340)(287,339)(288,345)
(289,344)(290,350)(291,349)(292,348)(293,347)(294,346)(295,359)(296,358)
(297,364)(298,363)(299,362)(300,361)(301,360)(302,352)(303,351)(304,357)
(305,356)(306,355)(307,354)(308,353)(309,380)(310,379)(311,385)(312,384)
(313,383)(314,382)(315,381)(316,387)(317,386)(318,392)(319,391)(320,390)
(321,389)(322,388)(323,366)(324,365)(325,371)(326,370)(327,369)(328,368)
(329,367)(330,373)(331,372)(332,378)(333,377)(334,376)(335,375)(336,374);;
s2 := (  1,225)(  2,226)(  3,227)(  4,228)(  5,229)(  6,230)(  7,231)(  8,232)
(  9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,246)( 16,247)
( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,239)( 23,240)( 24,241)
( 25,242)( 26,243)( 27,244)( 28,245)( 29,267)( 30,268)( 31,269)( 32,270)
( 33,271)( 34,272)( 35,273)( 36,274)( 37,275)( 38,276)( 39,277)( 40,278)
( 41,279)( 42,280)( 43,253)( 44,254)( 45,255)( 46,256)( 47,257)( 48,258)
( 49,259)( 50,260)( 51,261)( 52,262)( 53,263)( 54,264)( 55,265)( 56,266)
( 57,309)( 58,310)( 59,311)( 60,312)( 61,313)( 62,314)( 63,315)( 64,316)
( 65,317)( 66,318)( 67,319)( 68,320)( 69,321)( 70,322)( 71,330)( 72,331)
( 73,332)( 74,333)( 75,334)( 76,335)( 77,336)( 78,323)( 79,324)( 80,325)
( 81,326)( 82,327)( 83,328)( 84,329)( 85,281)( 86,282)( 87,283)( 88,284)
( 89,285)( 90,286)( 91,287)( 92,288)( 93,289)( 94,290)( 95,291)( 96,292)
( 97,293)( 98,294)( 99,302)(100,303)(101,304)(102,305)(103,306)(104,307)
(105,308)(106,295)(107,296)(108,297)(109,298)(110,299)(111,300)(112,301)
(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)
(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,358)(128,359)
(129,360)(130,361)(131,362)(132,363)(133,364)(134,351)(135,352)(136,353)
(137,354)(138,355)(139,356)(140,357)(141,379)(142,380)(143,381)(144,382)
(145,383)(146,384)(147,385)(148,386)(149,387)(150,388)(151,389)(152,390)
(153,391)(154,392)(155,365)(156,366)(157,367)(158,368)(159,369)(160,370)
(161,371)(162,372)(163,373)(164,374)(165,375)(166,376)(167,377)(168,378)
(169,421)(170,422)(171,423)(172,424)(173,425)(174,426)(175,427)(176,428)
(177,429)(178,430)(179,431)(180,432)(181,433)(182,434)(183,442)(184,443)
(185,444)(186,445)(187,446)(188,447)(189,448)(190,435)(191,436)(192,437)
(193,438)(194,439)(195,440)(196,441)(197,393)(198,394)(199,395)(200,396)
(201,397)(202,398)(203,399)(204,400)(205,401)(206,402)(207,403)(208,404)
(209,405)(210,406)(211,414)(212,415)(213,416)(214,417)(215,418)(216,419)
(217,420)(218,407)(219,408)(220,409)(221,410)(222,411)(223,412)(224,413);;
s3 := (449,450);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*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, 
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)!(  1,113)(  2,119)(  3,118)(  4,117)(  5,116)(  6,115)(  7,114)
(  8,120)(  9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,127)
( 16,133)( 17,132)( 18,131)( 19,130)( 20,129)( 21,128)( 22,134)( 23,140)
( 24,139)( 25,138)( 26,137)( 27,136)( 28,135)( 29,141)( 30,147)( 31,146)
( 32,145)( 33,144)( 34,143)( 35,142)( 36,148)( 37,154)( 38,153)( 39,152)
( 40,151)( 41,150)( 42,149)( 43,155)( 44,161)( 45,160)( 46,159)( 47,158)
( 48,157)( 49,156)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)
( 56,163)( 57,169)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)
( 64,176)( 65,182)( 66,181)( 67,180)( 68,179)( 69,178)( 70,177)( 71,183)
( 72,189)( 73,188)( 74,187)( 75,186)( 76,185)( 77,184)( 78,190)( 79,196)
( 80,195)( 81,194)( 82,193)( 83,192)( 84,191)( 85,197)( 86,203)( 87,202)
( 88,201)( 89,200)( 90,199)( 91,198)( 92,204)( 93,210)( 94,209)( 95,208)
( 96,207)( 97,206)( 98,205)( 99,211)(100,217)(101,216)(102,215)(103,214)
(104,213)(105,212)(106,218)(107,224)(108,223)(109,222)(110,221)(111,220)
(112,219)(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)
(232,344)(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,351)
(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,358)(247,364)
(248,363)(249,362)(250,361)(251,360)(252,359)(253,365)(254,371)(255,370)
(256,369)(257,368)(258,367)(259,366)(260,372)(261,378)(262,377)(263,376)
(264,375)(265,374)(266,373)(267,379)(268,385)(269,384)(270,383)(271,382)
(272,381)(273,380)(274,386)(275,392)(276,391)(277,390)(278,389)(279,388)
(280,387)(281,393)(282,399)(283,398)(284,397)(285,396)(286,395)(287,394)
(288,400)(289,406)(290,405)(291,404)(292,403)(293,402)(294,401)(295,407)
(296,413)(297,412)(298,411)(299,410)(300,409)(301,408)(302,414)(303,420)
(304,419)(305,418)(306,417)(307,416)(308,415)(309,421)(310,427)(311,426)
(312,425)(313,424)(314,423)(315,422)(316,428)(317,434)(318,433)(319,432)
(320,431)(321,430)(322,429)(323,435)(324,441)(325,440)(326,439)(327,438)
(328,437)(329,436)(330,442)(331,448)(332,447)(333,446)(334,445)(335,444)
(336,443);
s1 := Sym(450)!(  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)( 15,135)
( 16,134)( 17,140)( 18,139)( 19,138)( 20,137)( 21,136)( 22,128)( 23,127)
( 24,133)( 25,132)( 26,131)( 27,130)( 28,129)( 29,156)( 30,155)( 31,161)
( 32,160)( 33,159)( 34,158)( 35,157)( 36,163)( 37,162)( 38,168)( 39,167)
( 40,166)( 41,165)( 42,164)( 43,142)( 44,141)( 45,147)( 46,146)( 47,145)
( 48,144)( 49,143)( 50,149)( 51,148)( 52,154)( 53,153)( 54,152)( 55,151)
( 56,150)( 57,198)( 58,197)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)
( 64,205)( 65,204)( 66,210)( 67,209)( 68,208)( 69,207)( 70,206)( 71,219)
( 72,218)( 73,224)( 74,223)( 75,222)( 76,221)( 77,220)( 78,212)( 79,211)
( 80,217)( 81,216)( 82,215)( 83,214)( 84,213)( 85,170)( 86,169)( 87,175)
( 88,174)( 89,173)( 90,172)( 91,171)( 92,177)( 93,176)( 94,182)( 95,181)
( 96,180)( 97,179)( 98,178)( 99,191)(100,190)(101,196)(102,195)(103,194)
(104,193)(105,192)(106,184)(107,183)(108,189)(109,188)(110,187)(111,186)
(112,185)(225,394)(226,393)(227,399)(228,398)(229,397)(230,396)(231,395)
(232,401)(233,400)(234,406)(235,405)(236,404)(237,403)(238,402)(239,415)
(240,414)(241,420)(242,419)(243,418)(244,417)(245,416)(246,408)(247,407)
(248,413)(249,412)(250,411)(251,410)(252,409)(253,436)(254,435)(255,441)
(256,440)(257,439)(258,438)(259,437)(260,443)(261,442)(262,448)(263,447)
(264,446)(265,445)(266,444)(267,422)(268,421)(269,427)(270,426)(271,425)
(272,424)(273,423)(274,429)(275,428)(276,434)(277,433)(278,432)(279,431)
(280,430)(281,338)(282,337)(283,343)(284,342)(285,341)(286,340)(287,339)
(288,345)(289,344)(290,350)(291,349)(292,348)(293,347)(294,346)(295,359)
(296,358)(297,364)(298,363)(299,362)(300,361)(301,360)(302,352)(303,351)
(304,357)(305,356)(306,355)(307,354)(308,353)(309,380)(310,379)(311,385)
(312,384)(313,383)(314,382)(315,381)(316,387)(317,386)(318,392)(319,391)
(320,390)(321,389)(322,388)(323,366)(324,365)(325,371)(326,370)(327,369)
(328,368)(329,367)(330,373)(331,372)(332,378)(333,377)(334,376)(335,375)
(336,374);
s2 := Sym(450)!(  1,225)(  2,226)(  3,227)(  4,228)(  5,229)(  6,230)(  7,231)
(  8,232)(  9,233)( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,246)
( 16,247)( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,239)( 23,240)
( 24,241)( 25,242)( 26,243)( 27,244)( 28,245)( 29,267)( 30,268)( 31,269)
( 32,270)( 33,271)( 34,272)( 35,273)( 36,274)( 37,275)( 38,276)( 39,277)
( 40,278)( 41,279)( 42,280)( 43,253)( 44,254)( 45,255)( 46,256)( 47,257)
( 48,258)( 49,259)( 50,260)( 51,261)( 52,262)( 53,263)( 54,264)( 55,265)
( 56,266)( 57,309)( 58,310)( 59,311)( 60,312)( 61,313)( 62,314)( 63,315)
( 64,316)( 65,317)( 66,318)( 67,319)( 68,320)( 69,321)( 70,322)( 71,330)
( 72,331)( 73,332)( 74,333)( 75,334)( 76,335)( 77,336)( 78,323)( 79,324)
( 80,325)( 81,326)( 82,327)( 83,328)( 84,329)( 85,281)( 86,282)( 87,283)
( 88,284)( 89,285)( 90,286)( 91,287)( 92,288)( 93,289)( 94,290)( 95,291)
( 96,292)( 97,293)( 98,294)( 99,302)(100,303)(101,304)(102,305)(103,306)
(104,307)(105,308)(106,295)(107,296)(108,297)(109,298)(110,299)(111,300)
(112,301)(113,337)(114,338)(115,339)(116,340)(117,341)(118,342)(119,343)
(120,344)(121,345)(122,346)(123,347)(124,348)(125,349)(126,350)(127,358)
(128,359)(129,360)(130,361)(131,362)(132,363)(133,364)(134,351)(135,352)
(136,353)(137,354)(138,355)(139,356)(140,357)(141,379)(142,380)(143,381)
(144,382)(145,383)(146,384)(147,385)(148,386)(149,387)(150,388)(151,389)
(152,390)(153,391)(154,392)(155,365)(156,366)(157,367)(158,368)(159,369)
(160,370)(161,371)(162,372)(163,373)(164,374)(165,375)(166,376)(167,377)
(168,378)(169,421)(170,422)(171,423)(172,424)(173,425)(174,426)(175,427)
(176,428)(177,429)(178,430)(179,431)(180,432)(181,433)(182,434)(183,442)
(184,443)(185,444)(186,445)(187,446)(188,447)(189,448)(190,435)(191,436)
(192,437)(193,438)(194,439)(195,440)(196,441)(197,393)(198,394)(199,395)
(200,396)(201,397)(202,398)(203,399)(204,400)(205,401)(206,402)(207,403)
(208,404)(209,405)(210,406)(211,414)(212,415)(213,416)(214,417)(215,418)
(216,419)(217,420)(218,407)(219,408)(220,409)(221,410)(222,411)(223,412)
(224,413);
s3 := Sym(450)!(449,450);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*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, 
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