Polytope of Type {2,4,112}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,112}*1792a
if this polytope has a name.
Group : SmallGroup(1792,323306)
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, {2,2,112}*896
4-fold quotients : {2,4,28}*448, {2,2,56}*448
7-fold quotients : {2,4,16}*256a
8-fold quotients : {2,2,28}*224, {2,4,14}*224
14-fold quotients : {2,4,8}*128a, {2,2,16}*128
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)
( 59,171)( 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);;
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)(339,423)(340,429)
(341,428)(342,427)(343,426)(344,425)(345,424)(346,430)(347,436)(348,435)
(349,434)(350,433)(351,432)(352,431)(353,444)(354,450)(355,449)(356,448)
(357,447)(358,446)(359,445)(360,437)(361,443)(362,442)(363,441)(364,440)
(365,439)(366,438)(367,395)(368,401)(369,400)(370,399)(371,398)(372,397)
(373,396)(374,402)(375,408)(376,407)(377,406)(378,405)(379,404)(380,403)
(381,416)(382,422)(383,421)(384,420)(385,419)(386,418)(387,417)(388,409)
(389,415)(390,414)(391,413)(392,412)(393,411)(394,410);;
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)( 31,256)( 32,255)( 33,261)( 34,260)
( 35,259)( 36,258)( 37,257)( 38,263)( 39,262)( 40,268)( 41,267)( 42,266)
( 43,265)( 44,264)( 45,277)( 46,276)( 47,282)( 48,281)( 49,280)( 50,279)
( 51,278)( 52,270)( 53,269)( 54,275)( 55,274)( 56,273)( 57,272)( 58,271)
( 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)( 87,326)( 88,325)( 89,331)( 90,330)
( 91,329)( 92,328)( 93,327)( 94,333)( 95,332)( 96,338)( 97,337)( 98,336)
( 99,335)(100,334)(101,312)(102,311)(103,317)(104,316)(105,315)(106,314)
(107,313)(108,319)(109,318)(110,324)(111,323)(112,322)(113,321)(114,320)
(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)(143,368)(144,367)(145,373)(146,372)
(147,371)(148,370)(149,369)(150,375)(151,374)(152,380)(153,379)(154,378)
(155,377)(156,376)(157,389)(158,388)(159,394)(160,393)(161,392)(162,391)
(163,390)(164,382)(165,381)(166,387)(167,386)(168,385)(169,384)(170,383)
(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)(199,438)(200,437)(201,443)(202,442)
(203,441)(204,440)(205,439)(206,445)(207,444)(208,450)(209,449)(210,448)
(211,447)(212,446)(213,424)(214,423)(215,429)(216,428)(217,427)(218,426)
(219,425)(220,431)(221,430)(222,436)(223,435)(224,434)(225,433)(226,432);;
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, s1*s2*s3*s2*s1*s2*s3*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*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*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)( 4,116)( 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);
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)(339,423)
(340,429)(341,428)(342,427)(343,426)(344,425)(345,424)(346,430)(347,436)
(348,435)(349,434)(350,433)(351,432)(352,431)(353,444)(354,450)(355,449)
(356,448)(357,447)(358,446)(359,445)(360,437)(361,443)(362,442)(363,441)
(364,440)(365,439)(366,438)(367,395)(368,401)(369,400)(370,399)(371,398)
(372,397)(373,396)(374,402)(375,408)(376,407)(377,406)(378,405)(379,404)
(380,403)(381,416)(382,422)(383,421)(384,420)(385,419)(386,418)(387,417)
(388,409)(389,415)(390,414)(391,413)(392,412)(393,411)(394,410);
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)( 31,256)( 32,255)( 33,261)
( 34,260)( 35,259)( 36,258)( 37,257)( 38,263)( 39,262)( 40,268)( 41,267)
( 42,266)( 43,265)( 44,264)( 45,277)( 46,276)( 47,282)( 48,281)( 49,280)
( 50,279)( 51,278)( 52,270)( 53,269)( 54,275)( 55,274)( 56,273)( 57,272)
( 58,271)( 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)( 87,326)( 88,325)( 89,331)
( 90,330)( 91,329)( 92,328)( 93,327)( 94,333)( 95,332)( 96,338)( 97,337)
( 98,336)( 99,335)(100,334)(101,312)(102,311)(103,317)(104,316)(105,315)
(106,314)(107,313)(108,319)(109,318)(110,324)(111,323)(112,322)(113,321)
(114,320)(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)(143,368)(144,367)(145,373)
(146,372)(147,371)(148,370)(149,369)(150,375)(151,374)(152,380)(153,379)
(154,378)(155,377)(156,376)(157,389)(158,388)(159,394)(160,393)(161,392)
(162,391)(163,390)(164,382)(165,381)(166,387)(167,386)(168,385)(169,384)
(170,383)(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)(199,438)(200,437)(201,443)
(202,442)(203,441)(204,440)(205,439)(206,445)(207,444)(208,450)(209,449)
(210,448)(211,447)(212,446)(213,424)(214,423)(215,429)(216,428)(217,427)
(218,426)(219,425)(220,431)(221,430)(222,436)(223,435)(224,434)(225,433)
(226,432);
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,
s1*s2*s3*s2*s1*s2*s3*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*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*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