Polytope of Type {2,8,56}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,56}*1792d
if this polytope has a name.
Group : SmallGroup(1792,150684)
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}*896b
4-fold quotients : {2,4,28}*448
7-fold quotients : {2,8,8}*256d
8-fold quotients : {2,2,28}*224, {2,4,14}*224
14-fold quotients : {2,4,8}*128b, {2,8,4}*128b
16-fold quotients : {2,2,14}*112
28-fold quotients : {2,4,4}*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)( 31,164)( 32,165)( 33,166)( 34,167)
( 35,168)( 36,169)( 37,170)( 38,157)( 39,158)( 40,159)( 41,160)( 42,161)
( 43,162)( 44,163)( 45,150)( 46,151)( 47,152)( 48,153)( 49,154)( 50,155)
( 51,156)( 52,143)( 53,144)( 54,145)( 55,146)( 56,147)( 57,148)( 58,149)
( 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)( 87,213)( 88,214)( 89,215)( 90,216)
( 91,217)( 92,218)( 93,219)( 94,220)( 95,221)( 96,222)( 97,223)( 98,224)
( 99,225)(100,226)(101,199)(102,200)(103,201)(104,202)(105,203)(106,204)
(107,205)(108,206)(109,207)(110,208)(111,209)(112,210)(113,211)(114,212)
(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)(255,388)(256,389)(257,390)(258,391)
(259,392)(260,393)(261,394)(262,381)(263,382)(264,383)(265,384)(266,385)
(267,386)(268,387)(269,374)(270,375)(271,376)(272,377)(273,378)(274,379)
(275,380)(276,367)(277,368)(278,369)(279,370)(280,371)(281,372)(282,373)
(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)(311,437)(312,438)(313,439)(314,440)
(315,441)(316,442)(317,443)(318,444)(319,445)(320,446)(321,447)(322,448)
(323,449)(324,450)(325,423)(326,424)(327,425)(328,426)(329,427)(330,428)
(331,429)(332,430)(333,431)(334,432)(335,433)(336,434)(337,435)(338,436);;
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, 52)( 32, 58)( 33, 57)( 34, 56)
( 35, 55)( 36, 54)( 37, 53)( 38, 45)( 39, 51)( 40, 50)( 41, 49)( 42, 48)
( 43, 47)( 44, 46)( 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, 94)( 88,100)( 89, 99)( 90, 98)( 91, 97)( 92, 96)( 93, 95)(101,108)
(102,114)(103,113)(104,112)(105,111)(106,110)(107,109)(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)(255,332)(256,338)(257,337)(258,336)(259,335)(260,334)
(261,333)(262,325)(263,331)(264,330)(265,329)(266,328)(267,327)(268,326)
(269,318)(270,324)(271,323)(272,322)(273,321)(274,320)(275,319)(276,311)
(277,317)(278,316)(279,315)(280,314)(281,313)(282,312)(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,
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,
s2*s1*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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*s3*s2*s3*s1*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)( 31,164)( 32,165)( 33,166)
( 34,167)( 35,168)( 36,169)( 37,170)( 38,157)( 39,158)( 40,159)( 41,160)
( 42,161)( 43,162)( 44,163)( 45,150)( 46,151)( 47,152)( 48,153)( 49,154)
( 50,155)( 51,156)( 52,143)( 53,144)( 54,145)( 55,146)( 56,147)( 57,148)
( 58,149)( 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)( 87,213)( 88,214)( 89,215)
( 90,216)( 91,217)( 92,218)( 93,219)( 94,220)( 95,221)( 96,222)( 97,223)
( 98,224)( 99,225)(100,226)(101,199)(102,200)(103,201)(104,202)(105,203)
(106,204)(107,205)(108,206)(109,207)(110,208)(111,209)(112,210)(113,211)
(114,212)(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)(255,388)(256,389)(257,390)
(258,391)(259,392)(260,393)(261,394)(262,381)(263,382)(264,383)(265,384)
(266,385)(267,386)(268,387)(269,374)(270,375)(271,376)(272,377)(273,378)
(274,379)(275,380)(276,367)(277,368)(278,369)(279,370)(280,371)(281,372)
(282,373)(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)(311,437)(312,438)(313,439)
(314,440)(315,441)(316,442)(317,443)(318,444)(319,445)(320,446)(321,447)
(322,448)(323,449)(324,450)(325,423)(326,424)(327,425)(328,426)(329,427)
(330,428)(331,429)(332,430)(333,431)(334,432)(335,433)(336,434)(337,435)
(338,436);
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, 52)( 32, 58)( 33, 57)
( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 45)( 39, 51)( 40, 50)( 41, 49)
( 42, 48)( 43, 47)( 44, 46)( 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, 94)( 88,100)( 89, 99)( 90, 98)( 91, 97)( 92, 96)( 93, 95)
(101,108)(102,114)(103,113)(104,112)(105,111)(106,110)(107,109)(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)(255,332)(256,338)(257,337)(258,336)(259,335)
(260,334)(261,333)(262,325)(263,331)(264,330)(265,329)(266,328)(267,327)
(268,326)(269,318)(270,324)(271,323)(272,322)(273,321)(274,320)(275,319)
(276,311)(277,317)(278,316)(279,315)(280,314)(281,313)(282,312)(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, 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,
s2*s1*s3*s2*s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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*s3*s2*s3*s1*s2*s3*s2*s3 >;
to this polytope