Polytope of Type {28,8,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,8,2}*1792a
if this polytope has a name.
Group : SmallGroup(1792,141633)
Rank : 4
Schlafli Type : {28,8,2}
Number of vertices, edges, etc : 56, 224, 16, 2
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 : {28,4,2}*896, {28,8,2}*896a, {28,8,2}*896b
4-fold quotients : {28,4,2}*448, {14,8,2}*448
7-fold quotients : {4,8,2}*256a
8-fold quotients : {28,2,2}*224, {14,4,2}*224
14-fold quotients : {4,8,2}*128a, {4,8,2}*128b, {4,4,2}*128
16-fold quotients : {14,2,2}*112
28-fold quotients : {4,4,2}*64, {2,8,2}*64
32-fold quotients : {7,2,2}*56
56-fold quotients : {2,4,2}*32, {4,2,2}*32
112-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,113)( 2,119)( 3,118)( 4,117)( 5,116)( 6,115)( 7,114)( 8,120)
( 9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,127)( 16,133)
( 17,132)( 18,131)( 19,130)( 20,129)( 21,128)( 22,134)( 23,140)( 24,139)
( 25,138)( 26,137)( 27,136)( 28,135)( 29,141)( 30,147)( 31,146)( 32,145)
( 33,144)( 34,143)( 35,142)( 36,148)( 37,154)( 38,153)( 39,152)( 40,151)
( 41,150)( 42,149)( 43,155)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)
( 49,156)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)
( 57,176)( 58,182)( 59,181)( 60,180)( 61,179)( 62,178)( 63,177)( 64,169)
( 65,175)( 66,174)( 67,173)( 68,172)( 69,171)( 70,170)( 71,190)( 72,196)
( 73,195)( 74,194)( 75,193)( 76,192)( 77,191)( 78,183)( 79,189)( 80,188)
( 81,187)( 82,186)( 83,185)( 84,184)( 85,204)( 86,210)( 87,209)( 88,208)
( 89,207)( 90,206)( 91,205)( 92,197)( 93,203)( 94,202)( 95,201)( 96,200)
( 97,199)( 98,198)( 99,218)(100,224)(101,223)(102,222)(103,221)(104,220)
(105,219)(106,211)(107,217)(108,216)(109,215)(110,214)(111,213)(112,212)
(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,344)
(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,351)(240,357)
(241,356)(242,355)(243,354)(244,353)(245,352)(246,358)(247,364)(248,363)
(249,362)(250,361)(251,360)(252,359)(253,365)(254,371)(255,370)(256,369)
(257,368)(258,367)(259,366)(260,372)(261,378)(262,377)(263,376)(264,375)
(265,374)(266,373)(267,379)(268,385)(269,384)(270,383)(271,382)(272,381)
(273,380)(274,386)(275,392)(276,391)(277,390)(278,389)(279,388)(280,387)
(281,400)(282,406)(283,405)(284,404)(285,403)(286,402)(287,401)(288,393)
(289,399)(290,398)(291,397)(292,396)(293,395)(294,394)(295,414)(296,420)
(297,419)(298,418)(299,417)(300,416)(301,415)(302,407)(303,413)(304,412)
(305,411)(306,410)(307,409)(308,408)(309,428)(310,434)(311,433)(312,432)
(313,431)(314,430)(315,429)(316,421)(317,427)(318,426)(319,425)(320,424)
(321,423)(322,422)(323,442)(324,448)(325,447)(326,446)(327,445)(328,444)
(329,443)(330,435)(331,441)(332,440)(333,439)(334,438)(335,437)(336,436);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)
( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)
( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)
( 57, 72)( 58, 71)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 73)( 64, 79)
( 65, 78)( 66, 84)( 67, 83)( 68, 82)( 69, 81)( 70, 80)( 85,100)( 86, 99)
( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,107)( 93,106)( 94,112)
( 95,111)( 96,110)( 97,109)( 98,108)(113,142)(114,141)(115,147)(116,146)
(117,145)(118,144)(119,143)(120,149)(121,148)(122,154)(123,153)(124,152)
(125,151)(126,150)(127,156)(128,155)(129,161)(130,160)(131,159)(132,158)
(133,157)(134,163)(135,162)(136,168)(137,167)(138,166)(139,165)(140,164)
(169,212)(170,211)(171,217)(172,216)(173,215)(174,214)(175,213)(176,219)
(177,218)(178,224)(179,223)(180,222)(181,221)(182,220)(183,198)(184,197)
(185,203)(186,202)(187,201)(188,200)(189,199)(190,205)(191,204)(192,210)
(193,209)(194,208)(195,207)(196,206)(225,282)(226,281)(227,287)(228,286)
(229,285)(230,284)(231,283)(232,289)(233,288)(234,294)(235,293)(236,292)
(237,291)(238,290)(239,296)(240,295)(241,301)(242,300)(243,299)(244,298)
(245,297)(246,303)(247,302)(248,308)(249,307)(250,306)(251,305)(252,304)
(253,310)(254,309)(255,315)(256,314)(257,313)(258,312)(259,311)(260,317)
(261,316)(262,322)(263,321)(264,320)(265,319)(266,318)(267,324)(268,323)
(269,329)(270,328)(271,327)(272,326)(273,325)(274,331)(275,330)(276,336)
(277,335)(278,334)(279,333)(280,332)(337,429)(338,428)(339,434)(340,433)
(341,432)(342,431)(343,430)(344,422)(345,421)(346,427)(347,426)(348,425)
(349,424)(350,423)(351,443)(352,442)(353,448)(354,447)(355,446)(356,445)
(357,444)(358,436)(359,435)(360,441)(361,440)(362,439)(363,438)(364,437)
(365,401)(366,400)(367,406)(368,405)(369,404)(370,403)(371,402)(372,394)
(373,393)(374,399)(375,398)(376,397)(377,396)(378,395)(379,415)(380,414)
(381,420)(382,419)(383,418)(384,417)(385,416)(386,408)(387,407)(388,413)
(389,412)(390,411)(391,410)(392,409);;
s2 := ( 1,225)( 2,226)( 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)( 29,260)( 30,261)( 31,262)( 32,263)
( 33,264)( 34,265)( 35,266)( 36,253)( 37,254)( 38,255)( 39,256)( 40,257)
( 41,258)( 42,259)( 43,274)( 44,275)( 45,276)( 46,277)( 47,278)( 48,279)
( 49,280)( 50,267)( 51,268)( 52,269)( 53,270)( 54,271)( 55,272)( 56,273)
( 57,295)( 58,296)( 59,297)( 60,298)( 61,299)( 62,300)( 63,301)( 64,302)
( 65,303)( 66,304)( 67,305)( 68,306)( 69,307)( 70,308)( 71,281)( 72,282)
( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,289)( 80,290)
( 81,291)( 82,292)( 83,293)( 84,294)( 85,330)( 86,331)( 87,332)( 88,333)
( 89,334)( 90,335)( 91,336)( 92,323)( 93,324)( 94,325)( 95,326)( 96,327)
( 97,328)( 98,329)( 99,316)(100,317)(101,318)(102,319)(103,320)(104,321)
(105,322)(106,309)(107,310)(108,311)(109,312)(110,313)(111,314)(112,315)
(113,337)(114,338)(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)(141,372)(142,373)(143,374)(144,375)
(145,376)(146,377)(147,378)(148,365)(149,366)(150,367)(151,368)(152,369)
(153,370)(154,371)(155,386)(156,387)(157,388)(158,389)(159,390)(160,391)
(161,392)(162,379)(163,380)(164,381)(165,382)(166,383)(167,384)(168,385)
(169,407)(170,408)(171,409)(172,410)(173,411)(174,412)(175,413)(176,414)
(177,415)(178,416)(179,417)(180,418)(181,419)(182,420)(183,393)(184,394)
(185,395)(186,396)(187,397)(188,398)(189,399)(190,400)(191,401)(192,402)
(193,403)(194,404)(195,405)(196,406)(197,442)(198,443)(199,444)(200,445)
(201,446)(202,447)(203,448)(204,435)(205,436)(206,437)(207,438)(208,439)
(209,440)(210,441)(211,428)(212,429)(213,430)(214,431)(215,432)(216,433)
(217,434)(218,421)(219,422)(220,423)(221,424)(222,425)(223,426)(224,427);;
s3 := (449,450);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(450)!( 1,113)( 2,119)( 3,118)( 4,117)( 5,116)( 6,115)( 7,114)
( 8,120)( 9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,127)
( 16,133)( 17,132)( 18,131)( 19,130)( 20,129)( 21,128)( 22,134)( 23,140)
( 24,139)( 25,138)( 26,137)( 27,136)( 28,135)( 29,141)( 30,147)( 31,146)
( 32,145)( 33,144)( 34,143)( 35,142)( 36,148)( 37,154)( 38,153)( 39,152)
( 40,151)( 41,150)( 42,149)( 43,155)( 44,161)( 45,160)( 46,159)( 47,158)
( 48,157)( 49,156)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)
( 56,163)( 57,176)( 58,182)( 59,181)( 60,180)( 61,179)( 62,178)( 63,177)
( 64,169)( 65,175)( 66,174)( 67,173)( 68,172)( 69,171)( 70,170)( 71,190)
( 72,196)( 73,195)( 74,194)( 75,193)( 76,192)( 77,191)( 78,183)( 79,189)
( 80,188)( 81,187)( 82,186)( 83,185)( 84,184)( 85,204)( 86,210)( 87,209)
( 88,208)( 89,207)( 90,206)( 91,205)( 92,197)( 93,203)( 94,202)( 95,201)
( 96,200)( 97,199)( 98,198)( 99,218)(100,224)(101,223)(102,222)(103,221)
(104,220)(105,219)(106,211)(107,217)(108,216)(109,215)(110,214)(111,213)
(112,212)(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)
(232,344)(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,351)
(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,358)(247,364)
(248,363)(249,362)(250,361)(251,360)(252,359)(253,365)(254,371)(255,370)
(256,369)(257,368)(258,367)(259,366)(260,372)(261,378)(262,377)(263,376)
(264,375)(265,374)(266,373)(267,379)(268,385)(269,384)(270,383)(271,382)
(272,381)(273,380)(274,386)(275,392)(276,391)(277,390)(278,389)(279,388)
(280,387)(281,400)(282,406)(283,405)(284,404)(285,403)(286,402)(287,401)
(288,393)(289,399)(290,398)(291,397)(292,396)(293,395)(294,394)(295,414)
(296,420)(297,419)(298,418)(299,417)(300,416)(301,415)(302,407)(303,413)
(304,412)(305,411)(306,410)(307,409)(308,408)(309,428)(310,434)(311,433)
(312,432)(313,431)(314,430)(315,429)(316,421)(317,427)(318,426)(319,425)
(320,424)(321,423)(322,422)(323,442)(324,448)(325,447)(326,446)(327,445)
(328,444)(329,443)(330,435)(331,441)(332,440)(333,439)(334,438)(335,437)
(336,436);
s1 := Sym(450)!( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 16)
( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)
( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)
( 53, 55)( 57, 72)( 58, 71)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 73)
( 64, 79)( 65, 78)( 66, 84)( 67, 83)( 68, 82)( 69, 81)( 70, 80)( 85,100)
( 86, 99)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,107)( 93,106)
( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)(113,142)(114,141)(115,147)
(116,146)(117,145)(118,144)(119,143)(120,149)(121,148)(122,154)(123,153)
(124,152)(125,151)(126,150)(127,156)(128,155)(129,161)(130,160)(131,159)
(132,158)(133,157)(134,163)(135,162)(136,168)(137,167)(138,166)(139,165)
(140,164)(169,212)(170,211)(171,217)(172,216)(173,215)(174,214)(175,213)
(176,219)(177,218)(178,224)(179,223)(180,222)(181,221)(182,220)(183,198)
(184,197)(185,203)(186,202)(187,201)(188,200)(189,199)(190,205)(191,204)
(192,210)(193,209)(194,208)(195,207)(196,206)(225,282)(226,281)(227,287)
(228,286)(229,285)(230,284)(231,283)(232,289)(233,288)(234,294)(235,293)
(236,292)(237,291)(238,290)(239,296)(240,295)(241,301)(242,300)(243,299)
(244,298)(245,297)(246,303)(247,302)(248,308)(249,307)(250,306)(251,305)
(252,304)(253,310)(254,309)(255,315)(256,314)(257,313)(258,312)(259,311)
(260,317)(261,316)(262,322)(263,321)(264,320)(265,319)(266,318)(267,324)
(268,323)(269,329)(270,328)(271,327)(272,326)(273,325)(274,331)(275,330)
(276,336)(277,335)(278,334)(279,333)(280,332)(337,429)(338,428)(339,434)
(340,433)(341,432)(342,431)(343,430)(344,422)(345,421)(346,427)(347,426)
(348,425)(349,424)(350,423)(351,443)(352,442)(353,448)(354,447)(355,446)
(356,445)(357,444)(358,436)(359,435)(360,441)(361,440)(362,439)(363,438)
(364,437)(365,401)(366,400)(367,406)(368,405)(369,404)(370,403)(371,402)
(372,394)(373,393)(374,399)(375,398)(376,397)(377,396)(378,395)(379,415)
(380,414)(381,420)(382,419)(383,418)(384,417)(385,416)(386,408)(387,407)
(388,413)(389,412)(390,411)(391,410)(392,409);
s2 := Sym(450)!( 1,225)( 2,226)( 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)( 29,260)( 30,261)( 31,262)
( 32,263)( 33,264)( 34,265)( 35,266)( 36,253)( 37,254)( 38,255)( 39,256)
( 40,257)( 41,258)( 42,259)( 43,274)( 44,275)( 45,276)( 46,277)( 47,278)
( 48,279)( 49,280)( 50,267)( 51,268)( 52,269)( 53,270)( 54,271)( 55,272)
( 56,273)( 57,295)( 58,296)( 59,297)( 60,298)( 61,299)( 62,300)( 63,301)
( 64,302)( 65,303)( 66,304)( 67,305)( 68,306)( 69,307)( 70,308)( 71,281)
( 72,282)( 73,283)( 74,284)( 75,285)( 76,286)( 77,287)( 78,288)( 79,289)
( 80,290)( 81,291)( 82,292)( 83,293)( 84,294)( 85,330)( 86,331)( 87,332)
( 88,333)( 89,334)( 90,335)( 91,336)( 92,323)( 93,324)( 94,325)( 95,326)
( 96,327)( 97,328)( 98,329)( 99,316)(100,317)(101,318)(102,319)(103,320)
(104,321)(105,322)(106,309)(107,310)(108,311)(109,312)(110,313)(111,314)
(112,315)(113,337)(114,338)(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)(141,372)(142,373)(143,374)
(144,375)(145,376)(146,377)(147,378)(148,365)(149,366)(150,367)(151,368)
(152,369)(153,370)(154,371)(155,386)(156,387)(157,388)(158,389)(159,390)
(160,391)(161,392)(162,379)(163,380)(164,381)(165,382)(166,383)(167,384)
(168,385)(169,407)(170,408)(171,409)(172,410)(173,411)(174,412)(175,413)
(176,414)(177,415)(178,416)(179,417)(180,418)(181,419)(182,420)(183,393)
(184,394)(185,395)(186,396)(187,397)(188,398)(189,399)(190,400)(191,401)
(192,402)(193,403)(194,404)(195,405)(196,406)(197,442)(198,443)(199,444)
(200,445)(201,446)(202,447)(203,448)(204,435)(205,436)(206,437)(207,438)
(208,439)(209,440)(210,441)(211,428)(212,429)(213,430)(214,431)(215,432)
(216,433)(217,434)(218,421)(219,422)(220,423)(221,424)(222,425)(223,426)
(224,427);
s3 := Sym(450)!(449,450);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope