Polytope of Type {2,8,56}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,56}*1792a
if this polytope has a name.
Group : SmallGroup(1792,145173)
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}*896b, {2,8,28}*896a
4-fold quotients : {2,4,28}*448, {2,8,14}*448
7-fold quotients : {2,8,8}*256c
8-fold quotients : {2,2,28}*224, {2,4,14}*224
14-fold quotients : {2,8,4}*128a, {2,4,8}*128b
16-fold quotients : {2,2,14}*112
28-fold quotients : {2,4,4}*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 := ( 3,227)( 4,228)( 5,229)( 6,230)( 7,231)( 8,232)( 9,233)( 10,234)
( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)( 17,241)( 18,242)
( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)( 24,248)( 25,249)( 26,250)
( 27,251)( 28,252)( 29,253)( 30,254)( 31,262)( 32,263)( 33,264)( 34,265)
( 35,266)( 36,267)( 37,268)( 38,255)( 39,256)( 40,257)( 41,258)( 42,259)
( 43,260)( 44,261)( 45,276)( 46,277)( 47,278)( 48,279)( 49,280)( 50,281)
( 51,282)( 52,269)( 53,270)( 54,271)( 55,272)( 56,273)( 57,274)( 58,275)
( 59,297)( 60,298)( 61,299)( 62,300)( 63,301)( 64,302)( 65,303)( 66,304)
( 67,305)( 68,306)( 69,307)( 70,308)( 71,309)( 72,310)( 73,283)( 74,284)
( 75,285)( 76,286)( 77,287)( 78,288)( 79,289)( 80,290)( 81,291)( 82,292)
( 83,293)( 84,294)( 85,295)( 86,296)( 87,332)( 88,333)( 89,334)( 90,335)
( 91,336)( 92,337)( 93,338)( 94,325)( 95,326)( 96,327)( 97,328)( 98,329)
( 99,330)(100,331)(101,318)(102,319)(103,320)(104,321)(105,322)(106,323)
(107,324)(108,311)(109,312)(110,313)(111,314)(112,315)(113,316)(114,317)
(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)(121,345)(122,346)
(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)(129,353)(130,354)
(131,355)(132,356)(133,357)(134,358)(135,359)(136,360)(137,361)(138,362)
(139,363)(140,364)(141,365)(142,366)(143,374)(144,375)(145,376)(146,377)
(147,378)(148,379)(149,380)(150,367)(151,368)(152,369)(153,370)(154,371)
(155,372)(156,373)(157,388)(158,389)(159,390)(160,391)(161,392)(162,393)
(163,394)(164,381)(165,382)(166,383)(167,384)(168,385)(169,386)(170,387)
(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)(177,415)(178,416)
(179,417)(180,418)(181,419)(182,420)(183,421)(184,422)(185,395)(186,396)
(187,397)(188,398)(189,399)(190,400)(191,401)(192,402)(193,403)(194,404)
(195,405)(196,406)(197,407)(198,408)(199,444)(200,445)(201,446)(202,447)
(203,448)(204,449)(205,450)(206,437)(207,438)(208,439)(209,440)(210,441)
(211,442)(212,443)(213,430)(214,431)(215,432)(216,433)(217,434)(218,435)
(219,436)(220,423)(221,424)(222,425)(223,426)(224,427)(225,428)(226,429);;
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 := ( 3,116)( 4,115)( 5,121)( 6,120)( 7,119)( 8,118)( 9,117)( 10,123)
( 11,122)( 12,128)( 13,127)( 14,126)( 15,125)( 16,124)( 17,130)( 18,129)
( 19,135)( 20,134)( 21,133)( 22,132)( 23,131)( 24,137)( 25,136)( 26,142)
( 27,141)( 28,140)( 29,139)( 30,138)( 31,151)( 32,150)( 33,156)( 34,155)
( 35,154)( 36,153)( 37,152)( 38,144)( 39,143)( 40,149)( 41,148)( 42,147)
( 43,146)( 44,145)( 45,165)( 46,164)( 47,170)( 48,169)( 49,168)( 50,167)
( 51,166)( 52,158)( 53,157)( 54,163)( 55,162)( 56,161)( 57,160)( 58,159)
( 59,179)( 60,178)( 61,184)( 62,183)( 63,182)( 64,181)( 65,180)( 66,172)
( 67,171)( 68,177)( 69,176)( 70,175)( 71,174)( 72,173)( 73,193)( 74,192)
( 75,198)( 76,197)( 77,196)( 78,195)( 79,194)( 80,186)( 81,185)( 82,191)
( 83,190)( 84,189)( 85,188)( 86,187)( 87,200)( 88,199)( 89,205)( 90,204)
( 91,203)( 92,202)( 93,201)( 94,207)( 95,206)( 96,212)( 97,211)( 98,210)
( 99,209)(100,208)(101,214)(102,213)(103,219)(104,218)(105,217)(106,216)
(107,215)(108,221)(109,220)(110,226)(111,225)(112,224)(113,223)(114,222)
(227,340)(228,339)(229,345)(230,344)(231,343)(232,342)(233,341)(234,347)
(235,346)(236,352)(237,351)(238,350)(239,349)(240,348)(241,354)(242,353)
(243,359)(244,358)(245,357)(246,356)(247,355)(248,361)(249,360)(250,366)
(251,365)(252,364)(253,363)(254,362)(255,375)(256,374)(257,380)(258,379)
(259,378)(260,377)(261,376)(262,368)(263,367)(264,373)(265,372)(266,371)
(267,370)(268,369)(269,389)(270,388)(271,394)(272,393)(273,392)(274,391)
(275,390)(276,382)(277,381)(278,387)(279,386)(280,385)(281,384)(282,383)
(283,403)(284,402)(285,408)(286,407)(287,406)(288,405)(289,404)(290,396)
(291,395)(292,401)(293,400)(294,399)(295,398)(296,397)(297,417)(298,416)
(299,422)(300,421)(301,420)(302,419)(303,418)(304,410)(305,409)(306,415)
(307,414)(308,413)(309,412)(310,411)(311,424)(312,423)(313,429)(314,428)
(315,427)(316,426)(317,425)(318,431)(319,430)(320,436)(321,435)(322,434)
(323,433)(324,432)(325,438)(326,437)(327,443)(328,442)(329,441)(330,440)
(331,439)(332,445)(333,444)(334,450)(335,449)(336,448)(337,447)(338,446);;
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,
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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)!( 3,227)( 4,228)( 5,229)( 6,230)( 7,231)( 8,232)( 9,233)
( 10,234)( 11,235)( 12,236)( 13,237)( 14,238)( 15,239)( 16,240)( 17,241)
( 18,242)( 19,243)( 20,244)( 21,245)( 22,246)( 23,247)( 24,248)( 25,249)
( 26,250)( 27,251)( 28,252)( 29,253)( 30,254)( 31,262)( 32,263)( 33,264)
( 34,265)( 35,266)( 36,267)( 37,268)( 38,255)( 39,256)( 40,257)( 41,258)
( 42,259)( 43,260)( 44,261)( 45,276)( 46,277)( 47,278)( 48,279)( 49,280)
( 50,281)( 51,282)( 52,269)( 53,270)( 54,271)( 55,272)( 56,273)( 57,274)
( 58,275)( 59,297)( 60,298)( 61,299)( 62,300)( 63,301)( 64,302)( 65,303)
( 66,304)( 67,305)( 68,306)( 69,307)( 70,308)( 71,309)( 72,310)( 73,283)
( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,289)( 80,290)( 81,291)
( 82,292)( 83,293)( 84,294)( 85,295)( 86,296)( 87,332)( 88,333)( 89,334)
( 90,335)( 91,336)( 92,337)( 93,338)( 94,325)( 95,326)( 96,327)( 97,328)
( 98,329)( 99,330)(100,331)(101,318)(102,319)(103,320)(104,321)(105,322)
(106,323)(107,324)(108,311)(109,312)(110,313)(111,314)(112,315)(113,316)
(114,317)(115,339)(116,340)(117,341)(118,342)(119,343)(120,344)(121,345)
(122,346)(123,347)(124,348)(125,349)(126,350)(127,351)(128,352)(129,353)
(130,354)(131,355)(132,356)(133,357)(134,358)(135,359)(136,360)(137,361)
(138,362)(139,363)(140,364)(141,365)(142,366)(143,374)(144,375)(145,376)
(146,377)(147,378)(148,379)(149,380)(150,367)(151,368)(152,369)(153,370)
(154,371)(155,372)(156,373)(157,388)(158,389)(159,390)(160,391)(161,392)
(162,393)(163,394)(164,381)(165,382)(166,383)(167,384)(168,385)(169,386)
(170,387)(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)(177,415)
(178,416)(179,417)(180,418)(181,419)(182,420)(183,421)(184,422)(185,395)
(186,396)(187,397)(188,398)(189,399)(190,400)(191,401)(192,402)(193,403)
(194,404)(195,405)(196,406)(197,407)(198,408)(199,444)(200,445)(201,446)
(202,447)(203,448)(204,449)(205,450)(206,437)(207,438)(208,439)(209,440)
(210,441)(211,442)(212,443)(213,430)(214,431)(215,432)(216,433)(217,434)
(218,435)(219,436)(220,423)(221,424)(222,425)(223,426)(224,427)(225,428)
(226,429);
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)!( 3,116)( 4,115)( 5,121)( 6,120)( 7,119)( 8,118)( 9,117)
( 10,123)( 11,122)( 12,128)( 13,127)( 14,126)( 15,125)( 16,124)( 17,130)
( 18,129)( 19,135)( 20,134)( 21,133)( 22,132)( 23,131)( 24,137)( 25,136)
( 26,142)( 27,141)( 28,140)( 29,139)( 30,138)( 31,151)( 32,150)( 33,156)
( 34,155)( 35,154)( 36,153)( 37,152)( 38,144)( 39,143)( 40,149)( 41,148)
( 42,147)( 43,146)( 44,145)( 45,165)( 46,164)( 47,170)( 48,169)( 49,168)
( 50,167)( 51,166)( 52,158)( 53,157)( 54,163)( 55,162)( 56,161)( 57,160)
( 58,159)( 59,179)( 60,178)( 61,184)( 62,183)( 63,182)( 64,181)( 65,180)
( 66,172)( 67,171)( 68,177)( 69,176)( 70,175)( 71,174)( 72,173)( 73,193)
( 74,192)( 75,198)( 76,197)( 77,196)( 78,195)( 79,194)( 80,186)( 81,185)
( 82,191)( 83,190)( 84,189)( 85,188)( 86,187)( 87,200)( 88,199)( 89,205)
( 90,204)( 91,203)( 92,202)( 93,201)( 94,207)( 95,206)( 96,212)( 97,211)
( 98,210)( 99,209)(100,208)(101,214)(102,213)(103,219)(104,218)(105,217)
(106,216)(107,215)(108,221)(109,220)(110,226)(111,225)(112,224)(113,223)
(114,222)(227,340)(228,339)(229,345)(230,344)(231,343)(232,342)(233,341)
(234,347)(235,346)(236,352)(237,351)(238,350)(239,349)(240,348)(241,354)
(242,353)(243,359)(244,358)(245,357)(246,356)(247,355)(248,361)(249,360)
(250,366)(251,365)(252,364)(253,363)(254,362)(255,375)(256,374)(257,380)
(258,379)(259,378)(260,377)(261,376)(262,368)(263,367)(264,373)(265,372)
(266,371)(267,370)(268,369)(269,389)(270,388)(271,394)(272,393)(273,392)
(274,391)(275,390)(276,382)(277,381)(278,387)(279,386)(280,385)(281,384)
(282,383)(283,403)(284,402)(285,408)(286,407)(287,406)(288,405)(289,404)
(290,396)(291,395)(292,401)(293,400)(294,399)(295,398)(296,397)(297,417)
(298,416)(299,422)(300,421)(301,420)(302,419)(303,418)(304,410)(305,409)
(306,415)(307,414)(308,413)(309,412)(310,411)(311,424)(312,423)(313,429)
(314,428)(315,427)(316,426)(317,425)(318,431)(319,430)(320,436)(321,435)
(322,434)(323,433)(324,432)(325,438)(326,437)(327,443)(328,442)(329,441)
(330,440)(331,439)(332,445)(333,444)(334,450)(335,449)(336,448)(337,447)
(338,446);
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, s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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