Polytope of Type {2,112,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,112,4}*1792a
if this polytope has a name.
Group : SmallGroup(1792,323306)
Rank : 4
Schlafli Type : {2,112,4}
Number of vertices, edges, etc : 2, 112, 224, 4
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 : {2,56,4}*896a, {2,112,2}*896
4-fold quotients : {2,28,4}*448, {2,56,2}*448
7-fold quotients : {2,16,4}*256a
8-fold quotients : {2,28,2}*224, {2,14,4}*224
14-fold quotients : {2,8,4}*128a, {2,16,2}*128
16-fold quotients : {2,14,2}*112
28-fold quotients : {2,4,4}*64, {2,8,2}*64
32-fold quotients : {2,7,2}*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 := ( 3,227)( 4,233)( 5,232)( 6,231)( 7,230)( 8,229)( 9,228)( 10,234)
( 11,240)( 12,239)( 13,238)( 14,237)( 15,236)( 16,235)( 17,248)( 18,254)
( 19,253)( 20,252)( 21,251)( 22,250)( 23,249)( 24,241)( 25,247)( 26,246)
( 27,245)( 28,244)( 29,243)( 30,242)( 31,255)( 32,261)( 33,260)( 34,259)
( 35,258)( 36,257)( 37,256)( 38,262)( 39,268)( 40,267)( 41,266)( 42,265)
( 43,264)( 44,263)( 45,276)( 46,282)( 47,281)( 48,280)( 49,279)( 50,278)
( 51,277)( 52,269)( 53,275)( 54,274)( 55,273)( 56,272)( 57,271)( 58,270)
( 59,297)( 60,303)( 61,302)( 62,301)( 63,300)( 64,299)( 65,298)( 66,304)
( 67,310)( 68,309)( 69,308)( 70,307)( 71,306)( 72,305)( 73,283)( 74,289)
( 75,288)( 76,287)( 77,286)( 78,285)( 79,284)( 80,290)( 81,296)( 82,295)
( 83,294)( 84,293)( 85,292)( 86,291)( 87,325)( 88,331)( 89,330)( 90,329)
( 91,328)( 92,327)( 93,326)( 94,332)( 95,338)( 96,337)( 97,336)( 98,335)
( 99,334)(100,333)(101,311)(102,317)(103,316)(104,315)(105,314)(106,313)
(107,312)(108,318)(109,324)(110,323)(111,322)(112,321)(113,320)(114,319)
(115,339)(116,345)(117,344)(118,343)(119,342)(120,341)(121,340)(122,346)
(123,352)(124,351)(125,350)(126,349)(127,348)(128,347)(129,360)(130,366)
(131,365)(132,364)(133,363)(134,362)(135,361)(136,353)(137,359)(138,358)
(139,357)(140,356)(141,355)(142,354)(143,367)(144,373)(145,372)(146,371)
(147,370)(148,369)(149,368)(150,374)(151,380)(152,379)(153,378)(154,377)
(155,376)(156,375)(157,388)(158,394)(159,393)(160,392)(161,391)(162,390)
(163,389)(164,381)(165,387)(166,386)(167,385)(168,384)(169,383)(170,382)
(171,409)(172,415)(173,414)(174,413)(175,412)(176,411)(177,410)(178,416)
(179,422)(180,421)(181,420)(182,419)(183,418)(184,417)(185,395)(186,401)
(187,400)(188,399)(189,398)(190,397)(191,396)(192,402)(193,408)(194,407)
(195,406)(196,405)(197,404)(198,403)(199,437)(200,443)(201,442)(202,441)
(203,440)(204,439)(205,438)(206,444)(207,450)(208,449)(209,448)(210,447)
(211,446)(212,445)(213,423)(214,429)(215,428)(216,427)(217,426)(218,425)
(219,424)(220,430)(221,436)(222,435)(223,434)(224,433)(225,432)(226,431);;
s2 := ( 3, 4)( 5, 9)( 6, 8)( 10, 11)( 12, 16)( 13, 15)( 17, 25)( 18, 24)
( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 31, 32)( 33, 37)( 34, 36)
( 38, 39)( 40, 44)( 41, 43)( 45, 53)( 46, 52)( 47, 58)( 48, 57)( 49, 56)
( 50, 55)( 51, 54)( 59, 74)( 60, 73)( 61, 79)( 62, 78)( 63, 77)( 64, 76)
( 65, 75)( 66, 81)( 67, 80)( 68, 86)( 69, 85)( 70, 84)( 71, 83)( 72, 82)
( 87,102)( 88,101)( 89,107)( 90,106)( 91,105)( 92,104)( 93,103)( 94,109)
( 95,108)( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(115,144)(116,143)
(117,149)(118,148)(119,147)(120,146)(121,145)(122,151)(123,150)(124,156)
(125,155)(126,154)(127,153)(128,152)(129,165)(130,164)(131,170)(132,169)
(133,168)(134,167)(135,166)(136,158)(137,157)(138,163)(139,162)(140,161)
(141,160)(142,159)(171,214)(172,213)(173,219)(174,218)(175,217)(176,216)
(177,215)(178,221)(179,220)(180,226)(181,225)(182,224)(183,223)(184,222)
(185,200)(186,199)(187,205)(188,204)(189,203)(190,202)(191,201)(192,207)
(193,206)(194,212)(195,211)(196,210)(197,209)(198,208)(227,284)(228,283)
(229,289)(230,288)(231,287)(232,286)(233,285)(234,291)(235,290)(236,296)
(237,295)(238,294)(239,293)(240,292)(241,305)(242,304)(243,310)(244,309)
(245,308)(246,307)(247,306)(248,298)(249,297)(250,303)(251,302)(252,301)
(253,300)(254,299)(255,312)(256,311)(257,317)(258,316)(259,315)(260,314)
(261,313)(262,319)(263,318)(264,324)(265,323)(266,322)(267,321)(268,320)
(269,333)(270,332)(271,338)(272,337)(273,336)(274,335)(275,334)(276,326)
(277,325)(278,331)(279,330)(280,329)(281,328)(282,327)(339,424)(340,423)
(341,429)(342,428)(343,427)(344,426)(345,425)(346,431)(347,430)(348,436)
(349,435)(350,434)(351,433)(352,432)(353,445)(354,444)(355,450)(356,449)
(357,448)(358,447)(359,446)(360,438)(361,437)(362,443)(363,442)(364,441)
(365,440)(366,439)(367,396)(368,395)(369,401)(370,400)(371,399)(372,398)
(373,397)(374,403)(375,402)(376,408)(377,407)(378,406)(379,405)(380,404)
(381,417)(382,416)(383,422)(384,421)(385,420)(386,419)(387,418)(388,410)
(389,409)(390,415)(391,414)(392,413)(393,412)(394,411);;
s3 := ( 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)
( 59,171)( 60,172)( 61,173)( 62,174)( 63,175)( 64,176)( 65,177)( 66,178)
( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)( 72,184)( 73,185)( 74,186)
( 75,187)( 76,188)( 77,189)( 78,190)( 79,191)( 80,192)( 81,193)( 82,194)
( 83,195)( 84,196)( 85,197)( 86,198)( 87,199)( 88,200)( 89,201)( 90,202)
( 91,203)( 92,204)( 93,205)( 94,206)( 95,207)( 96,208)( 97,209)( 98,210)
( 99,211)(100,212)(101,213)(102,214)(103,215)(104,216)(105,217)(106,218)
(107,219)(108,220)(109,221)(110,222)(111,223)(112,224)(113,225)(114,226)
(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)
(283,395)(284,396)(285,397)(286,398)(287,399)(288,400)(289,401)(290,402)
(291,403)(292,404)(293,405)(294,406)(295,407)(296,408)(297,409)(298,410)
(299,411)(300,412)(301,413)(302,414)(303,415)(304,416)(305,417)(306,418)
(307,419)(308,420)(309,421)(310,422)(311,423)(312,424)(313,425)(314,426)
(315,427)(316,428)(317,429)(318,430)(319,431)(320,432)(321,433)(322,434)
(323,435)(324,436)(325,437)(326,438)(327,439)(328,440)(329,441)(330,442)
(331,443)(332,444)(333,445)(334,446)(335,447)(336,448)(337,449)(338,450);;
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*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,
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*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*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*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)!( 3,227)( 4,233)( 5,232)( 6,231)( 7,230)( 8,229)( 9,228)
( 10,234)( 11,240)( 12,239)( 13,238)( 14,237)( 15,236)( 16,235)( 17,248)
( 18,254)( 19,253)( 20,252)( 21,251)( 22,250)( 23,249)( 24,241)( 25,247)
( 26,246)( 27,245)( 28,244)( 29,243)( 30,242)( 31,255)( 32,261)( 33,260)
( 34,259)( 35,258)( 36,257)( 37,256)( 38,262)( 39,268)( 40,267)( 41,266)
( 42,265)( 43,264)( 44,263)( 45,276)( 46,282)( 47,281)( 48,280)( 49,279)
( 50,278)( 51,277)( 52,269)( 53,275)( 54,274)( 55,273)( 56,272)( 57,271)
( 58,270)( 59,297)( 60,303)( 61,302)( 62,301)( 63,300)( 64,299)( 65,298)
( 66,304)( 67,310)( 68,309)( 69,308)( 70,307)( 71,306)( 72,305)( 73,283)
( 74,289)( 75,288)( 76,287)( 77,286)( 78,285)( 79,284)( 80,290)( 81,296)
( 82,295)( 83,294)( 84,293)( 85,292)( 86,291)( 87,325)( 88,331)( 89,330)
( 90,329)( 91,328)( 92,327)( 93,326)( 94,332)( 95,338)( 96,337)( 97,336)
( 98,335)( 99,334)(100,333)(101,311)(102,317)(103,316)(104,315)(105,314)
(106,313)(107,312)(108,318)(109,324)(110,323)(111,322)(112,321)(113,320)
(114,319)(115,339)(116,345)(117,344)(118,343)(119,342)(120,341)(121,340)
(122,346)(123,352)(124,351)(125,350)(126,349)(127,348)(128,347)(129,360)
(130,366)(131,365)(132,364)(133,363)(134,362)(135,361)(136,353)(137,359)
(138,358)(139,357)(140,356)(141,355)(142,354)(143,367)(144,373)(145,372)
(146,371)(147,370)(148,369)(149,368)(150,374)(151,380)(152,379)(153,378)
(154,377)(155,376)(156,375)(157,388)(158,394)(159,393)(160,392)(161,391)
(162,390)(163,389)(164,381)(165,387)(166,386)(167,385)(168,384)(169,383)
(170,382)(171,409)(172,415)(173,414)(174,413)(175,412)(176,411)(177,410)
(178,416)(179,422)(180,421)(181,420)(182,419)(183,418)(184,417)(185,395)
(186,401)(187,400)(188,399)(189,398)(190,397)(191,396)(192,402)(193,408)
(194,407)(195,406)(196,405)(197,404)(198,403)(199,437)(200,443)(201,442)
(202,441)(203,440)(204,439)(205,438)(206,444)(207,450)(208,449)(209,448)
(210,447)(211,446)(212,445)(213,423)(214,429)(215,428)(216,427)(217,426)
(218,425)(219,424)(220,430)(221,436)(222,435)(223,434)(224,433)(225,432)
(226,431);
s2 := Sym(450)!( 3, 4)( 5, 9)( 6, 8)( 10, 11)( 12, 16)( 13, 15)( 17, 25)
( 18, 24)( 19, 30)( 20, 29)( 21, 28)( 22, 27)( 23, 26)( 31, 32)( 33, 37)
( 34, 36)( 38, 39)( 40, 44)( 41, 43)( 45, 53)( 46, 52)( 47, 58)( 48, 57)
( 49, 56)( 50, 55)( 51, 54)( 59, 74)( 60, 73)( 61, 79)( 62, 78)( 63, 77)
( 64, 76)( 65, 75)( 66, 81)( 67, 80)( 68, 86)( 69, 85)( 70, 84)( 71, 83)
( 72, 82)( 87,102)( 88,101)( 89,107)( 90,106)( 91,105)( 92,104)( 93,103)
( 94,109)( 95,108)( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(115,144)
(116,143)(117,149)(118,148)(119,147)(120,146)(121,145)(122,151)(123,150)
(124,156)(125,155)(126,154)(127,153)(128,152)(129,165)(130,164)(131,170)
(132,169)(133,168)(134,167)(135,166)(136,158)(137,157)(138,163)(139,162)
(140,161)(141,160)(142,159)(171,214)(172,213)(173,219)(174,218)(175,217)
(176,216)(177,215)(178,221)(179,220)(180,226)(181,225)(182,224)(183,223)
(184,222)(185,200)(186,199)(187,205)(188,204)(189,203)(190,202)(191,201)
(192,207)(193,206)(194,212)(195,211)(196,210)(197,209)(198,208)(227,284)
(228,283)(229,289)(230,288)(231,287)(232,286)(233,285)(234,291)(235,290)
(236,296)(237,295)(238,294)(239,293)(240,292)(241,305)(242,304)(243,310)
(244,309)(245,308)(246,307)(247,306)(248,298)(249,297)(250,303)(251,302)
(252,301)(253,300)(254,299)(255,312)(256,311)(257,317)(258,316)(259,315)
(260,314)(261,313)(262,319)(263,318)(264,324)(265,323)(266,322)(267,321)
(268,320)(269,333)(270,332)(271,338)(272,337)(273,336)(274,335)(275,334)
(276,326)(277,325)(278,331)(279,330)(280,329)(281,328)(282,327)(339,424)
(340,423)(341,429)(342,428)(343,427)(344,426)(345,425)(346,431)(347,430)
(348,436)(349,435)(350,434)(351,433)(352,432)(353,445)(354,444)(355,450)
(356,449)(357,448)(358,447)(359,446)(360,438)(361,437)(362,443)(363,442)
(364,441)(365,440)(366,439)(367,396)(368,395)(369,401)(370,400)(371,399)
(372,398)(373,397)(374,403)(375,402)(376,408)(377,407)(378,406)(379,405)
(380,404)(381,417)(382,416)(383,422)(384,421)(385,420)(386,419)(387,418)
(388,410)(389,409)(390,415)(391,414)(392,413)(393,412)(394,411);
s3 := 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)( 59,171)( 60,172)( 61,173)( 62,174)( 63,175)( 64,176)( 65,177)
( 66,178)( 67,179)( 68,180)( 69,181)( 70,182)( 71,183)( 72,184)( 73,185)
( 74,186)( 75,187)( 76,188)( 77,189)( 78,190)( 79,191)( 80,192)( 81,193)
( 82,194)( 83,195)( 84,196)( 85,197)( 86,198)( 87,199)( 88,200)( 89,201)
( 90,202)( 91,203)( 92,204)( 93,205)( 94,206)( 95,207)( 96,208)( 97,209)
( 98,210)( 99,211)(100,212)(101,213)(102,214)(103,215)(104,216)(105,217)
(106,218)(107,219)(108,220)(109,221)(110,222)(111,223)(112,224)(113,225)
(114,226)(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)(283,395)(284,396)(285,397)(286,398)(287,399)(288,400)(289,401)
(290,402)(291,403)(292,404)(293,405)(294,406)(295,407)(296,408)(297,409)
(298,410)(299,411)(300,412)(301,413)(302,414)(303,415)(304,416)(305,417)
(306,418)(307,419)(308,420)(309,421)(310,422)(311,423)(312,424)(313,425)
(314,426)(315,427)(316,428)(317,429)(318,430)(319,431)(320,432)(321,433)
(322,434)(323,435)(324,436)(325,437)(326,438)(327,439)(328,440)(329,441)
(330,442)(331,443)(332,444)(333,445)(334,446)(335,447)(336,448)(337,449)
(338,450);
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*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, 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*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*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*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