Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,56,2}

Atlas Canonical Name {8,56,2}*1792b

Overview

Group
SmallGroup(1792,145174)
Rank
4
Schläfli Type
{8,56,2}
Vertices, edges, …
8, 224, 56, 2
Order of s0s1s2s3
56
Order of s0s1s2s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-fold

7-fold

8-fold

14-fold

16-fold

28-fold

32-fold

56-fold

112-fold

Covers minimal covers in bold

None in this atlas.

Representations

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