Overview
- Group
- SmallGroup(1792,150684)
- Rank
- 4
- Schläfli Type
- {2,8,56}
- Vertices, edges, …
- 2, 8, 224, 56
- 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 := (1,2);; 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,
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2,
s1*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,
s2*s3*s2*s3*s1*s2*s3*s2*s3*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*s1*s2*s3*s1*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)( 31,164)( 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, s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2, s1*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, s2*s3*s2*s3*s1*s2*s3*s2*s3*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*s1*s2*s3*s1*s2*s3*s2*s3*s2*s3 >;