Polytope of Type {2,4,112}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,112}*1792b
if this polytope has a name.
Group : SmallGroup(1792,323454)
Rank : 4
Schlafli Type : {2,4,112}
Number of vertices, edges, etc : 2, 4, 224, 112
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 : {2,4,56}*896a
4-fold quotients : {2,4,28}*448, {2,2,56}*448
7-fold quotients : {2,4,16}*256b
8-fold quotients : {2,2,28}*224, {2,4,14}*224
14-fold quotients : {2,4,8}*128a
16-fold quotients : {2,2,14}*112
28-fold quotients : {2,4,4}*64, {2,2,8}*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 := ( 3,115)( 4,116)( 5,117)( 6,118)( 7,119)( 8,120)( 9,121)( 10,122)
( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)( 17,129)( 18,130)
( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)( 24,136)( 25,137)( 26,138)
( 27,139)( 28,140)( 29,141)( 30,142)( 31,143)( 32,144)( 33,145)( 34,146)
( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)( 40,152)( 41,153)( 42,154)
( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)( 48,160)( 49,161)( 50,162)
( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)( 56,168)( 57,169)( 58,170)
( 59,178)( 60,179)( 61,180)( 62,181)( 63,182)( 64,183)( 65,184)( 66,171)
( 67,172)( 68,173)( 69,174)( 70,175)( 71,176)( 72,177)( 73,192)( 74,193)
( 75,194)( 76,195)( 77,196)( 78,197)( 79,198)( 80,185)( 81,186)( 82,187)
( 83,188)( 84,189)( 85,190)( 86,191)( 87,206)( 88,207)( 89,208)( 90,209)
( 91,210)( 92,211)( 93,212)( 94,199)( 95,200)( 96,201)( 97,202)( 98,203)
( 99,204)(100,205)(101,220)(102,221)(103,222)(104,223)(105,224)(106,225)
(107,226)(108,213)(109,214)(110,215)(111,216)(112,217)(113,218)(114,219)
(227,339)(228,340)(229,341)(230,342)(231,343)(232,344)(233,345)(234,346)
(235,347)(236,348)(237,349)(238,350)(239,351)(240,352)(241,353)(242,354)
(243,355)(244,356)(245,357)(246,358)(247,359)(248,360)(249,361)(250,362)
(251,363)(252,364)(253,365)(254,366)(255,367)(256,368)(257,369)(258,370)
(259,371)(260,372)(261,373)(262,374)(263,375)(264,376)(265,377)(266,378)
(267,379)(268,380)(269,381)(270,382)(271,383)(272,384)(273,385)(274,386)
(275,387)(276,388)(277,389)(278,390)(279,391)(280,392)(281,393)(282,394)
(283,402)(284,403)(285,404)(286,405)(287,406)(288,407)(289,408)(290,395)
(291,396)(292,397)(293,398)(294,399)(295,400)(296,401)(297,416)(298,417)
(299,418)(300,419)(301,420)(302,421)(303,422)(304,409)(305,410)(306,411)
(307,412)(308,413)(309,414)(310,415)(311,430)(312,431)(313,432)(314,433)
(315,434)(316,435)(317,436)(318,423)(319,424)(320,425)(321,426)(322,427)
(323,428)(324,429)(325,444)(326,445)(327,446)(328,447)(329,448)(330,449)
(331,450)(332,437)(333,438)(334,439)(335,440)(336,441)(337,442)(338,443);;
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 := ( 3,228)( 4,227)( 5,233)( 6,232)( 7,231)( 8,230)( 9,229)( 10,235)
( 11,234)( 12,240)( 13,239)( 14,238)( 15,237)( 16,236)( 17,249)( 18,248)
( 19,254)( 20,253)( 21,252)( 22,251)( 23,250)( 24,242)( 25,241)( 26,247)
( 27,246)( 28,245)( 29,244)( 30,243)( 31,263)( 32,262)( 33,268)( 34,267)
( 35,266)( 36,265)( 37,264)( 38,256)( 39,255)( 40,261)( 41,260)( 42,259)
( 43,258)( 44,257)( 45,270)( 46,269)( 47,275)( 48,274)( 49,273)( 50,272)
( 51,271)( 52,277)( 53,276)( 54,282)( 55,281)( 56,280)( 57,279)( 58,278)
( 59,298)( 60,297)( 61,303)( 62,302)( 63,301)( 64,300)( 65,299)( 66,305)
( 67,304)( 68,310)( 69,309)( 70,308)( 71,307)( 72,306)( 73,284)( 74,283)
( 75,289)( 76,288)( 77,287)( 78,286)( 79,285)( 80,291)( 81,290)( 82,296)
( 83,295)( 84,294)( 85,293)( 86,292)( 87,333)( 88,332)( 89,338)( 90,337)
( 91,336)( 92,335)( 93,334)( 94,326)( 95,325)( 96,331)( 97,330)( 98,329)
( 99,328)(100,327)(101,319)(102,318)(103,324)(104,323)(105,322)(106,321)
(107,320)(108,312)(109,311)(110,317)(111,316)(112,315)(113,314)(114,313)
(115,340)(116,339)(117,345)(118,344)(119,343)(120,342)(121,341)(122,347)
(123,346)(124,352)(125,351)(126,350)(127,349)(128,348)(129,361)(130,360)
(131,366)(132,365)(133,364)(134,363)(135,362)(136,354)(137,353)(138,359)
(139,358)(140,357)(141,356)(142,355)(143,375)(144,374)(145,380)(146,379)
(147,378)(148,377)(149,376)(150,368)(151,367)(152,373)(153,372)(154,371)
(155,370)(156,369)(157,382)(158,381)(159,387)(160,386)(161,385)(162,384)
(163,383)(164,389)(165,388)(166,394)(167,393)(168,392)(169,391)(170,390)
(171,410)(172,409)(173,415)(174,414)(175,413)(176,412)(177,411)(178,417)
(179,416)(180,422)(181,421)(182,420)(183,419)(184,418)(185,396)(186,395)
(187,401)(188,400)(189,399)(190,398)(191,397)(192,403)(193,402)(194,408)
(195,407)(196,406)(197,405)(198,404)(199,445)(200,444)(201,450)(202,449)
(203,448)(204,447)(205,446)(206,438)(207,437)(208,443)(209,442)(210,441)
(211,440)(212,439)(213,431)(214,430)(215,436)(216,435)(217,434)(218,433)
(219,432)(220,424)(221,423)(222,429)(223,428)(224,427)(225,426)(226,425);;
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*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2,
s1*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*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*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(450)!(1,2);
s1 := Sym(450)!( 3,115)( 4,116)( 5,117)( 6,118)( 7,119)( 8,120)( 9,121)
( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)( 17,129)
( 18,130)( 19,131)( 20,132)( 21,133)( 22,134)( 23,135)( 24,136)( 25,137)
( 26,138)( 27,139)( 28,140)( 29,141)( 30,142)( 31,143)( 32,144)( 33,145)
( 34,146)( 35,147)( 36,148)( 37,149)( 38,150)( 39,151)( 40,152)( 41,153)
( 42,154)( 43,155)( 44,156)( 45,157)( 46,158)( 47,159)( 48,160)( 49,161)
( 50,162)( 51,163)( 52,164)( 53,165)( 54,166)( 55,167)( 56,168)( 57,169)
( 58,170)( 59,178)( 60,179)( 61,180)( 62,181)( 63,182)( 64,183)( 65,184)
( 66,171)( 67,172)( 68,173)( 69,174)( 70,175)( 71,176)( 72,177)( 73,192)
( 74,193)( 75,194)( 76,195)( 77,196)( 78,197)( 79,198)( 80,185)( 81,186)
( 82,187)( 83,188)( 84,189)( 85,190)( 86,191)( 87,206)( 88,207)( 89,208)
( 90,209)( 91,210)( 92,211)( 93,212)( 94,199)( 95,200)( 96,201)( 97,202)
( 98,203)( 99,204)(100,205)(101,220)(102,221)(103,222)(104,223)(105,224)
(106,225)(107,226)(108,213)(109,214)(110,215)(111,216)(112,217)(113,218)
(114,219)(227,339)(228,340)(229,341)(230,342)(231,343)(232,344)(233,345)
(234,346)(235,347)(236,348)(237,349)(238,350)(239,351)(240,352)(241,353)
(242,354)(243,355)(244,356)(245,357)(246,358)(247,359)(248,360)(249,361)
(250,362)(251,363)(252,364)(253,365)(254,366)(255,367)(256,368)(257,369)
(258,370)(259,371)(260,372)(261,373)(262,374)(263,375)(264,376)(265,377)
(266,378)(267,379)(268,380)(269,381)(270,382)(271,383)(272,384)(273,385)
(274,386)(275,387)(276,388)(277,389)(278,390)(279,391)(280,392)(281,393)
(282,394)(283,402)(284,403)(285,404)(286,405)(287,406)(288,407)(289,408)
(290,395)(291,396)(292,397)(293,398)(294,399)(295,400)(296,401)(297,416)
(298,417)(299,418)(300,419)(301,420)(302,421)(303,422)(304,409)(305,410)
(306,411)(307,412)(308,413)(309,414)(310,415)(311,430)(312,431)(313,432)
(314,433)(315,434)(316,435)(317,436)(318,423)(319,424)(320,425)(321,426)
(322,427)(323,428)(324,429)(325,444)(326,445)(327,446)(328,447)(329,448)
(330,449)(331,450)(332,437)(333,438)(334,439)(335,440)(336,441)(337,442)
(338,443);
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)!( 3,228)( 4,227)( 5,233)( 6,232)( 7,231)( 8,230)( 9,229)
( 10,235)( 11,234)( 12,240)( 13,239)( 14,238)( 15,237)( 16,236)( 17,249)
( 18,248)( 19,254)( 20,253)( 21,252)( 22,251)( 23,250)( 24,242)( 25,241)
( 26,247)( 27,246)( 28,245)( 29,244)( 30,243)( 31,263)( 32,262)( 33,268)
( 34,267)( 35,266)( 36,265)( 37,264)( 38,256)( 39,255)( 40,261)( 41,260)
( 42,259)( 43,258)( 44,257)( 45,270)( 46,269)( 47,275)( 48,274)( 49,273)
( 50,272)( 51,271)( 52,277)( 53,276)( 54,282)( 55,281)( 56,280)( 57,279)
( 58,278)( 59,298)( 60,297)( 61,303)( 62,302)( 63,301)( 64,300)( 65,299)
( 66,305)( 67,304)( 68,310)( 69,309)( 70,308)( 71,307)( 72,306)( 73,284)
( 74,283)( 75,289)( 76,288)( 77,287)( 78,286)( 79,285)( 80,291)( 81,290)
( 82,296)( 83,295)( 84,294)( 85,293)( 86,292)( 87,333)( 88,332)( 89,338)
( 90,337)( 91,336)( 92,335)( 93,334)( 94,326)( 95,325)( 96,331)( 97,330)
( 98,329)( 99,328)(100,327)(101,319)(102,318)(103,324)(104,323)(105,322)
(106,321)(107,320)(108,312)(109,311)(110,317)(111,316)(112,315)(113,314)
(114,313)(115,340)(116,339)(117,345)(118,344)(119,343)(120,342)(121,341)
(122,347)(123,346)(124,352)(125,351)(126,350)(127,349)(128,348)(129,361)
(130,360)(131,366)(132,365)(133,364)(134,363)(135,362)(136,354)(137,353)
(138,359)(139,358)(140,357)(141,356)(142,355)(143,375)(144,374)(145,380)
(146,379)(147,378)(148,377)(149,376)(150,368)(151,367)(152,373)(153,372)
(154,371)(155,370)(156,369)(157,382)(158,381)(159,387)(160,386)(161,385)
(162,384)(163,383)(164,389)(165,388)(166,394)(167,393)(168,392)(169,391)
(170,390)(171,410)(172,409)(173,415)(174,414)(175,413)(176,412)(177,411)
(178,417)(179,416)(180,422)(181,421)(182,420)(183,419)(184,418)(185,396)
(186,395)(187,401)(188,400)(189,399)(190,398)(191,397)(192,403)(193,402)
(194,408)(195,407)(196,406)(197,405)(198,404)(199,445)(200,444)(201,450)
(202,449)(203,448)(204,447)(205,446)(206,438)(207,437)(208,443)(209,442)
(210,441)(211,440)(212,439)(213,431)(214,430)(215,436)(216,435)(217,434)
(218,433)(219,432)(220,424)(221,423)(222,429)(223,428)(224,427)(225,426)
(226,425);
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*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2,
s1*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*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*s1*s2*s3*s2 >;
to this polytope