Polytope of Type {2,8,56}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,56}*1792c
if this polytope has a name.
Group : SmallGroup(1792,145174)
Rank : 4
Schlafli Type : {2,8,56}
Number of vertices, edges, etc : 2, 8, 224, 56
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, {2,8,28}*896a
4-fold quotients : {2,4,28}*448, {2,2,56}*448, {2,8,14}*448
7-fold quotients : {2,8,8}*256b
8-fold quotients : {2,2,28}*224, {2,4,14}*224
14-fold quotients : {2,4,8}*128a, {2,8,4}*128a
16-fold quotients : {2,2,14}*112
28-fold quotients : {2,4,4}*64, {2,2,8}*64, {2,8,2}*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)( 31,150)( 32,151)( 33,152)( 34,153)
( 35,154)( 36,155)( 37,156)( 38,143)( 39,144)( 40,145)( 41,146)( 42,147)
( 43,148)( 44,149)( 45,164)( 46,165)( 47,166)( 48,167)( 49,168)( 50,169)
( 51,170)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)( 58,163)
( 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)( 87,199)( 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)(255,374)(256,375)(257,376)(258,377)
(259,378)(260,379)(261,380)(262,367)(263,368)(264,369)(265,370)(266,371)
(267,372)(268,373)(269,388)(270,389)(271,390)(272,391)(273,392)(274,393)
(275,394)(276,381)(277,382)(278,383)(279,384)(280,385)(281,386)(282,387)
(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)(311,423)(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)( 18, 23)( 19, 22)
( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 31, 38)( 32, 44)( 33, 43)( 34, 42)
( 35, 41)( 36, 40)( 37, 39)( 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)
( 87,108)( 88,114)( 89,113)( 90,112)( 91,111)( 92,110)( 93,109)( 94,101)
( 95,107)( 96,106)( 97,105)( 98,104)( 99,103)(100,102)(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)(255,318)(256,324)(257,323)(258,322)(259,321)(260,320)
(261,319)(262,311)(263,317)(264,316)(265,315)(266,314)(267,313)(268,312)
(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)(353,444)(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 := ( 3,340)( 4,339)( 5,345)( 6,344)( 7,343)( 8,342)( 9,341)( 10,347)
( 11,346)( 12,352)( 13,351)( 14,350)( 15,349)( 16,348)( 17,354)( 18,353)
( 19,359)( 20,358)( 21,357)( 22,356)( 23,355)( 24,361)( 25,360)( 26,366)
( 27,365)( 28,364)( 29,363)( 30,362)( 31,368)( 32,367)( 33,373)( 34,372)
( 35,371)( 36,370)( 37,369)( 38,375)( 39,374)( 40,380)( 41,379)( 42,378)
( 43,377)( 44,376)( 45,382)( 46,381)( 47,387)( 48,386)( 49,385)( 50,384)
( 51,383)( 52,389)( 53,388)( 54,394)( 55,393)( 56,392)( 57,391)( 58,390)
( 59,417)( 60,416)( 61,422)( 62,421)( 63,420)( 64,419)( 65,418)( 66,410)
( 67,409)( 68,415)( 69,414)( 70,413)( 71,412)( 72,411)( 73,403)( 74,402)
( 75,408)( 76,407)( 77,406)( 78,405)( 79,404)( 80,396)( 81,395)( 82,401)
( 83,400)( 84,399)( 85,398)( 86,397)( 87,445)( 88,444)( 89,450)( 90,449)
( 91,448)( 92,447)( 93,446)( 94,438)( 95,437)( 96,443)( 97,442)( 98,441)
( 99,440)(100,439)(101,431)(102,430)(103,436)(104,435)(105,434)(106,433)
(107,432)(108,424)(109,423)(110,429)(111,428)(112,427)(113,426)(114,425)
(115,228)(116,227)(117,233)(118,232)(119,231)(120,230)(121,229)(122,235)
(123,234)(124,240)(125,239)(126,238)(127,237)(128,236)(129,242)(130,241)
(131,247)(132,246)(133,245)(134,244)(135,243)(136,249)(137,248)(138,254)
(139,253)(140,252)(141,251)(142,250)(143,256)(144,255)(145,261)(146,260)
(147,259)(148,258)(149,257)(150,263)(151,262)(152,268)(153,267)(154,266)
(155,265)(156,264)(157,270)(158,269)(159,275)(160,274)(161,273)(162,272)
(163,271)(164,277)(165,276)(166,282)(167,281)(168,280)(169,279)(170,278)
(171,305)(172,304)(173,310)(174,309)(175,308)(176,307)(177,306)(178,298)
(179,297)(180,303)(181,302)(182,301)(183,300)(184,299)(185,291)(186,290)
(187,296)(188,295)(189,294)(190,293)(191,292)(192,284)(193,283)(194,289)
(195,288)(196,287)(197,286)(198,285)(199,333)(200,332)(201,338)(202,337)
(203,336)(204,335)(205,334)(206,326)(207,325)(208,331)(209,330)(210,329)
(211,328)(212,327)(213,319)(214,318)(215,324)(216,323)(217,322)(218,321)
(219,320)(220,312)(221,311)(222,317)(223,316)(224,315)(225,314)(226,313);;
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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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)( 31,150)( 32,151)( 33,152)
( 34,153)( 35,154)( 36,155)( 37,156)( 38,143)( 39,144)( 40,145)( 41,146)
( 42,147)( 43,148)( 44,149)( 45,164)( 46,165)( 47,166)( 48,167)( 49,168)
( 50,169)( 51,170)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)
( 58,163)( 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)( 87,199)( 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)(255,374)(256,375)(257,376)
(258,377)(259,378)(260,379)(261,380)(262,367)(263,368)(264,369)(265,370)
(266,371)(267,372)(268,373)(269,388)(270,389)(271,390)(272,391)(273,392)
(274,393)(275,394)(276,381)(277,382)(278,383)(279,384)(280,385)(281,386)
(282,387)(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)(311,423)(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)( 18, 23)
( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 31, 38)( 32, 44)( 33, 43)
( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 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)( 87,108)( 88,114)( 89,113)( 90,112)( 91,111)( 92,110)( 93,109)
( 94,101)( 95,107)( 96,106)( 97,105)( 98,104)( 99,103)(100,102)(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)(255,318)(256,324)(257,323)(258,322)(259,321)
(260,320)(261,319)(262,311)(263,317)(264,316)(265,315)(266,314)(267,313)
(268,312)(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)(353,444)(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)!( 3,340)( 4,339)( 5,345)( 6,344)( 7,343)( 8,342)( 9,341)
( 10,347)( 11,346)( 12,352)( 13,351)( 14,350)( 15,349)( 16,348)( 17,354)
( 18,353)( 19,359)( 20,358)( 21,357)( 22,356)( 23,355)( 24,361)( 25,360)
( 26,366)( 27,365)( 28,364)( 29,363)( 30,362)( 31,368)( 32,367)( 33,373)
( 34,372)( 35,371)( 36,370)( 37,369)( 38,375)( 39,374)( 40,380)( 41,379)
( 42,378)( 43,377)( 44,376)( 45,382)( 46,381)( 47,387)( 48,386)( 49,385)
( 50,384)( 51,383)( 52,389)( 53,388)( 54,394)( 55,393)( 56,392)( 57,391)
( 58,390)( 59,417)( 60,416)( 61,422)( 62,421)( 63,420)( 64,419)( 65,418)
( 66,410)( 67,409)( 68,415)( 69,414)( 70,413)( 71,412)( 72,411)( 73,403)
( 74,402)( 75,408)( 76,407)( 77,406)( 78,405)( 79,404)( 80,396)( 81,395)
( 82,401)( 83,400)( 84,399)( 85,398)( 86,397)( 87,445)( 88,444)( 89,450)
( 90,449)( 91,448)( 92,447)( 93,446)( 94,438)( 95,437)( 96,443)( 97,442)
( 98,441)( 99,440)(100,439)(101,431)(102,430)(103,436)(104,435)(105,434)
(106,433)(107,432)(108,424)(109,423)(110,429)(111,428)(112,427)(113,426)
(114,425)(115,228)(116,227)(117,233)(118,232)(119,231)(120,230)(121,229)
(122,235)(123,234)(124,240)(125,239)(126,238)(127,237)(128,236)(129,242)
(130,241)(131,247)(132,246)(133,245)(134,244)(135,243)(136,249)(137,248)
(138,254)(139,253)(140,252)(141,251)(142,250)(143,256)(144,255)(145,261)
(146,260)(147,259)(148,258)(149,257)(150,263)(151,262)(152,268)(153,267)
(154,266)(155,265)(156,264)(157,270)(158,269)(159,275)(160,274)(161,273)
(162,272)(163,271)(164,277)(165,276)(166,282)(167,281)(168,280)(169,279)
(170,278)(171,305)(172,304)(173,310)(174,309)(175,308)(176,307)(177,306)
(178,298)(179,297)(180,303)(181,302)(182,301)(183,300)(184,299)(185,291)
(186,290)(187,296)(188,295)(189,294)(190,293)(191,292)(192,284)(193,283)
(194,289)(195,288)(196,287)(197,286)(198,285)(199,333)(200,332)(201,338)
(202,337)(203,336)(204,335)(205,334)(206,326)(207,325)(208,331)(209,330)
(210,329)(211,328)(212,327)(213,319)(214,318)(215,324)(216,323)(217,322)
(218,321)(219,320)(220,312)(221,311)(222,317)(223,316)(224,315)(225,314)
(226,313);
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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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