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