Polytope of Type {2,4,56}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,56}*1792a
if this polytope has a name.
Group : SmallGroup(1792,141634)
Rank : 4
Schlafli Type : {2,4,56}
Number of vertices, edges, etc : 2, 8, 224, 112
Order of s0s1s2s3 : 56
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, {2,4,28}*896, {2,4,56}*896b
4-fold quotients : {2,4,28}*448, {2,2,56}*448
7-fold quotients : {2,4,8}*256a
8-fold quotients : {2,2,28}*224, {2,4,14}*224
14-fold quotients : {2,4,8}*128a, {2,4,8}*128b, {2,4,4}*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)
( 59,178)( 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)( 18, 23)( 19, 22)
( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)
( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)
( 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)(129,157)(130,163)(131,162)(132,161)(133,160)(134,159)
(135,158)(136,164)(137,170)(138,169)(139,168)(140,167)(141,166)(142,165)
(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)(241,297)(242,303)(243,302)(244,301)(245,300)(246,299)
(247,298)(248,304)(249,310)(250,309)(251,308)(252,307)(253,306)(254,305)
(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)(269,325)(270,331)
(271,330)(272,329)(273,328)(274,327)(275,326)(276,332)(277,338)(278,337)
(279,336)(280,335)(281,334)(282,333)(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)(353,444)(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)
(367,402)(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)(381,416)(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)( 17,242)( 18,241)
( 19,247)( 20,246)( 21,245)( 22,244)( 23,243)( 24,249)( 25,248)( 26,254)
( 27,253)( 28,252)( 29,251)( 30,250)( 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)( 45,277)( 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)( 87,333)( 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)(129,354)(130,353)
(131,359)(132,358)(133,357)(134,356)(135,355)(136,361)(137,360)(138,366)
(139,365)(140,364)(141,363)(142,362)(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)(157,389)(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)(199,445)(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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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)( 59,178)( 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)( 18, 23)
( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)
( 39, 44)( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)
( 55, 56)( 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)(129,157)(130,163)(131,162)(132,161)(133,160)
(134,159)(135,158)(136,164)(137,170)(138,169)(139,168)(140,167)(141,166)
(142,165)(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)(241,297)(242,303)(243,302)(244,301)(245,300)
(246,299)(247,298)(248,304)(249,310)(250,309)(251,308)(252,307)(253,306)
(254,305)(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)(269,325)
(270,331)(271,330)(272,329)(273,328)(274,327)(275,326)(276,332)(277,338)
(278,337)(279,336)(280,335)(281,334)(282,333)(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)(353,444)(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)(367,402)(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)(381,416)
(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)( 17,242)
( 18,241)( 19,247)( 20,246)( 21,245)( 22,244)( 23,243)( 24,249)( 25,248)
( 26,254)( 27,253)( 28,252)( 29,251)( 30,250)( 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)( 45,277)( 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)( 87,333)( 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)(129,354)
(130,353)(131,359)(132,358)(133,357)(134,356)(135,355)(136,361)(137,360)
(138,366)(139,365)(140,364)(141,363)(142,362)(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)(157,389)(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)(199,445)(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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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