Overview
- Group
- SmallGroup(1824,975)
- Rank
- 3
- Schläfli Type
- {114,8}
- Vertices, edges, …
- 114, 456, 8
- Order of s0s1s2
- 456
- Order of s0s1s2s1
- 2
- Also known as
- {114,8|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
19-fold
24-fold
38-fold
57-fold
76-fold
114-fold
152-fold
228-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 19)( 3, 18)( 4, 17)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 12)( 10, 11)( 20, 39)( 21, 57)( 22, 56)( 23, 55)( 24, 54)( 25, 53)( 26, 52)( 27, 51)( 28, 50)( 29, 49)( 30, 48)( 31, 47)( 32, 46)( 33, 45)( 34, 44)( 35, 43)( 36, 42)( 37, 41)( 38, 40)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 77, 96)( 78,114)( 79,113)( 80,112)( 81,111)( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)( 95, 97)(116,133)(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(134,153)(135,171)(136,170)(137,169)(138,168)(139,167)(140,166)(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)(147,159)(148,158)(149,157)(150,156)(151,155)(152,154)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)(180,183)(181,182)(191,210)(192,228)(193,227)(194,226)(195,225)(196,224)(197,223)(198,222)(199,221)(200,220)(201,219)(202,218)(203,217)(204,216)(205,215)(206,214)(207,213)(208,212)(209,211)(230,247)(231,246)(232,245)(233,244)(234,243)(235,242)(236,241)(237,240)(238,239)(248,267)(249,285)(250,284)(251,283)(252,282)(253,281)(254,280)(255,279)(256,278)(257,277)(258,276)(259,275)(260,274)(261,273)(262,272)(263,271)(264,270)(265,269)(266,268)(287,304)(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)(305,324)(306,342)(307,341)(308,340)(309,339)(310,338)(311,337)(312,336)(313,335)(314,334)(315,333)(316,332)(317,331)(318,330)(319,329)(320,328)(321,327)(322,326)(323,325)(344,361)(345,360)(346,359)(347,358)(348,357)(349,356)(350,355)(351,354)(352,353)(362,381)(363,399)(364,398)(365,397)(366,396)(367,395)(368,394)(369,393)(370,392)(371,391)(372,390)(373,389)(374,388)(375,387)(376,386)(377,385)(378,384)(379,383)(380,382)(401,418)(402,417)(403,416)(404,415)(405,414)(406,413)(407,412)(408,411)(409,410)(419,438)(420,456)(421,455)(422,454)(423,453)(424,452)(425,451)(426,450)(427,449)(428,448)(429,447)(430,446)(431,445)(432,444)(433,443)(434,442)(435,441)(436,440)(437,439);; s1 := ( 1, 21)( 2, 20)( 3, 38)( 4, 37)( 5, 36)( 6, 35)( 7, 34)( 8, 33)( 9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 58, 78)( 59, 77)( 60, 95)( 61, 94)( 62, 93)( 63, 92)( 64, 91)( 65, 90)( 66, 89)( 67, 88)( 68, 87)( 69, 86)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)( 96, 97)( 98,114)( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(115,192)(116,191)(117,209)(118,208)(119,207)(120,206)(121,205)(122,204)(123,203)(124,202)(125,201)(126,200)(127,199)(128,198)(129,197)(130,196)(131,195)(132,194)(133,193)(134,173)(135,172)(136,190)(137,189)(138,188)(139,187)(140,186)(141,185)(142,184)(143,183)(144,182)(145,181)(146,180)(147,179)(148,178)(149,177)(150,176)(151,175)(152,174)(153,211)(154,210)(155,228)(156,227)(157,226)(158,225)(159,224)(160,223)(161,222)(162,221)(163,220)(164,219)(165,218)(166,217)(167,216)(168,215)(169,214)(170,213)(171,212)(229,363)(230,362)(231,380)(232,379)(233,378)(234,377)(235,376)(236,375)(237,374)(238,373)(239,372)(240,371)(241,370)(242,369)(243,368)(244,367)(245,366)(246,365)(247,364)(248,344)(249,343)(250,361)(251,360)(252,359)(253,358)(254,357)(255,356)(256,355)(257,354)(258,353)(259,352)(260,351)(261,350)(262,349)(263,348)(264,347)(265,346)(266,345)(267,382)(268,381)(269,399)(270,398)(271,397)(272,396)(273,395)(274,394)(275,393)(276,392)(277,391)(278,390)(279,389)(280,388)(281,387)(282,386)(283,385)(284,384)(285,383)(286,420)(287,419)(288,437)(289,436)(290,435)(291,434)(292,433)(293,432)(294,431)(295,430)(296,429)(297,428)(298,427)(299,426)(300,425)(301,424)(302,423)(303,422)(304,421)(305,401)(306,400)(307,418)(308,417)(309,416)(310,415)(311,414)(312,413)(313,412)(314,411)(315,410)(316,409)(317,408)(318,407)(319,406)(320,405)(321,404)(322,403)(323,402)(324,439)(325,438)(326,456)(327,455)(328,454)(329,453)(330,452)(331,451)(332,450)(333,449)(334,448)(335,447)(336,446)(337,445)(338,444)(339,443)(340,442)(341,441)(342,440);; s2 := ( 1,229)( 2,230)( 3,231)( 4,232)( 5,233)( 6,234)( 7,235)( 8,236)( 9,237)( 10,238)( 11,239)( 12,240)( 13,241)( 14,242)( 15,243)( 16,244)( 17,245)( 18,246)( 19,247)( 20,248)( 21,249)( 22,250)( 23,251)( 24,252)( 25,253)( 26,254)( 27,255)( 28,256)( 29,257)( 30,258)( 31,259)( 32,260)( 33,261)( 34,262)( 35,263)( 36,264)( 37,265)( 38,266)( 39,267)( 40,268)( 41,269)( 42,270)( 43,271)( 44,272)( 45,273)( 46,274)( 47,275)( 48,276)( 49,277)( 50,278)( 51,279)( 52,280)( 53,281)( 54,282)( 55,283)( 56,284)( 57,285)( 58,286)( 59,287)( 60,288)( 61,289)( 62,290)( 63,291)( 64,292)( 65,293)( 66,294)( 67,295)( 68,296)( 69,297)( 70,298)( 71,299)( 72,300)( 73,301)( 74,302)( 75,303)( 76,304)( 77,305)( 78,306)( 79,307)( 80,308)( 81,309)( 82,310)( 83,311)( 84,312)( 85,313)( 86,314)( 87,315)( 88,316)( 89,317)( 90,318)( 91,319)( 92,320)( 93,321)( 94,322)( 95,323)( 96,324)( 97,325)( 98,326)( 99,327)(100,328)(101,329)(102,330)(103,331)(104,332)(105,333)(106,334)(107,335)(108,336)(109,337)(110,338)(111,339)(112,340)(113,341)(114,342)(115,400)(116,401)(117,402)(118,403)(119,404)(120,405)(121,406)(122,407)(123,408)(124,409)(125,410)(126,411)(127,412)(128,413)(129,414)(130,415)(131,416)(132,417)(133,418)(134,419)(135,420)(136,421)(137,422)(138,423)(139,424)(140,425)(141,426)(142,427)(143,428)(144,429)(145,430)(146,431)(147,432)(148,433)(149,434)(150,435)(151,436)(152,437)(153,438)(154,439)(155,440)(156,441)(157,442)(158,443)(159,444)(160,445)(161,446)(162,447)(163,448)(164,449)(165,450)(166,451)(167,452)(168,453)(169,454)(170,455)(171,456)(172,343)(173,344)(174,345)(175,346)(176,347)(177,348)(178,349)(179,350)(180,351)(181,352)(182,353)(183,354)(184,355)(185,356)(186,357)(187,358)(188,359)(189,360)(190,361)(191,362)(192,363)(193,364)(194,365)(195,366)(196,367)(197,368)(198,369)(199,370)(200,371)(201,372)(202,373)(203,374)(204,375)(205,376)(206,377)(207,378)(208,379)(209,380)(210,381)(211,382)(212,383)(213,384)(214,385)(215,386)(216,387)(217,388)(218,389)(219,390)(220,391)(221,392)(222,393)(223,394)(224,395)(225,396)(226,397)(227,398)(228,399);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*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*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*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*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*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(456)!( 2, 19)( 3, 18)( 4, 17)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 12)( 10, 11)( 20, 39)( 21, 57)( 22, 56)( 23, 55)( 24, 54)( 25, 53)( 26, 52)( 27, 51)( 28, 50)( 29, 49)( 30, 48)( 31, 47)( 32, 46)( 33, 45)( 34, 44)( 35, 43)( 36, 42)( 37, 41)( 38, 40)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 77, 96)( 78,114)( 79,113)( 80,112)( 81,111)( 82,110)( 83,109)( 84,108)( 85,107)( 86,106)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92,100)( 93, 99)( 94, 98)( 95, 97)(116,133)(117,132)(118,131)(119,130)(120,129)(121,128)(122,127)(123,126)(124,125)(134,153)(135,171)(136,170)(137,169)(138,168)(139,167)(140,166)(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)(147,159)(148,158)(149,157)(150,156)(151,155)(152,154)(173,190)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)(180,183)(181,182)(191,210)(192,228)(193,227)(194,226)(195,225)(196,224)(197,223)(198,222)(199,221)(200,220)(201,219)(202,218)(203,217)(204,216)(205,215)(206,214)(207,213)(208,212)(209,211)(230,247)(231,246)(232,245)(233,244)(234,243)(235,242)(236,241)(237,240)(238,239)(248,267)(249,285)(250,284)(251,283)(252,282)(253,281)(254,280)(255,279)(256,278)(257,277)(258,276)(259,275)(260,274)(261,273)(262,272)(263,271)(264,270)(265,269)(266,268)(287,304)(288,303)(289,302)(290,301)(291,300)(292,299)(293,298)(294,297)(295,296)(305,324)(306,342)(307,341)(308,340)(309,339)(310,338)(311,337)(312,336)(313,335)(314,334)(315,333)(316,332)(317,331)(318,330)(319,329)(320,328)(321,327)(322,326)(323,325)(344,361)(345,360)(346,359)(347,358)(348,357)(349,356)(350,355)(351,354)(352,353)(362,381)(363,399)(364,398)(365,397)(366,396)(367,395)(368,394)(369,393)(370,392)(371,391)(372,390)(373,389)(374,388)(375,387)(376,386)(377,385)(378,384)(379,383)(380,382)(401,418)(402,417)(403,416)(404,415)(405,414)(406,413)(407,412)(408,411)(409,410)(419,438)(420,456)(421,455)(422,454)(423,453)(424,452)(425,451)(426,450)(427,449)(428,448)(429,447)(430,446)(431,445)(432,444)(433,443)(434,442)(435,441)(436,440)(437,439); s1 := Sym(456)!( 1, 21)( 2, 20)( 3, 38)( 4, 37)( 5, 36)( 6, 35)( 7, 34)( 8, 33)( 9, 32)( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 39, 40)( 41, 57)( 42, 56)( 43, 55)( 44, 54)( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 58, 78)( 59, 77)( 60, 95)( 61, 94)( 62, 93)( 63, 92)( 64, 91)( 65, 90)( 66, 89)( 67, 88)( 68, 87)( 69, 86)( 70, 85)( 71, 84)( 72, 83)( 73, 82)( 74, 81)( 75, 80)( 76, 79)( 96, 97)( 98,114)( 99,113)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(115,192)(116,191)(117,209)(118,208)(119,207)(120,206)(121,205)(122,204)(123,203)(124,202)(125,201)(126,200)(127,199)(128,198)(129,197)(130,196)(131,195)(132,194)(133,193)(134,173)(135,172)(136,190)(137,189)(138,188)(139,187)(140,186)(141,185)(142,184)(143,183)(144,182)(145,181)(146,180)(147,179)(148,178)(149,177)(150,176)(151,175)(152,174)(153,211)(154,210)(155,228)(156,227)(157,226)(158,225)(159,224)(160,223)(161,222)(162,221)(163,220)(164,219)(165,218)(166,217)(167,216)(168,215)(169,214)(170,213)(171,212)(229,363)(230,362)(231,380)(232,379)(233,378)(234,377)(235,376)(236,375)(237,374)(238,373)(239,372)(240,371)(241,370)(242,369)(243,368)(244,367)(245,366)(246,365)(247,364)(248,344)(249,343)(250,361)(251,360)(252,359)(253,358)(254,357)(255,356)(256,355)(257,354)(258,353)(259,352)(260,351)(261,350)(262,349)(263,348)(264,347)(265,346)(266,345)(267,382)(268,381)(269,399)(270,398)(271,397)(272,396)(273,395)(274,394)(275,393)(276,392)(277,391)(278,390)(279,389)(280,388)(281,387)(282,386)(283,385)(284,384)(285,383)(286,420)(287,419)(288,437)(289,436)(290,435)(291,434)(292,433)(293,432)(294,431)(295,430)(296,429)(297,428)(298,427)(299,426)(300,425)(301,424)(302,423)(303,422)(304,421)(305,401)(306,400)(307,418)(308,417)(309,416)(310,415)(311,414)(312,413)(313,412)(314,411)(315,410)(316,409)(317,408)(318,407)(319,406)(320,405)(321,404)(322,403)(323,402)(324,439)(325,438)(326,456)(327,455)(328,454)(329,453)(330,452)(331,451)(332,450)(333,449)(334,448)(335,447)(336,446)(337,445)(338,444)(339,443)(340,442)(341,441)(342,440); s2 := Sym(456)!( 1,229)( 2,230)( 3,231)( 4,232)( 5,233)( 6,234)( 7,235)( 8,236)( 9,237)( 10,238)( 11,239)( 12,240)( 13,241)( 14,242)( 15,243)( 16,244)( 17,245)( 18,246)( 19,247)( 20,248)( 21,249)( 22,250)( 23,251)( 24,252)( 25,253)( 26,254)( 27,255)( 28,256)( 29,257)( 30,258)( 31,259)( 32,260)( 33,261)( 34,262)( 35,263)( 36,264)( 37,265)( 38,266)( 39,267)( 40,268)( 41,269)( 42,270)( 43,271)( 44,272)( 45,273)( 46,274)( 47,275)( 48,276)( 49,277)( 50,278)( 51,279)( 52,280)( 53,281)( 54,282)( 55,283)( 56,284)( 57,285)( 58,286)( 59,287)( 60,288)( 61,289)( 62,290)( 63,291)( 64,292)( 65,293)( 66,294)( 67,295)( 68,296)( 69,297)( 70,298)( 71,299)( 72,300)( 73,301)( 74,302)( 75,303)( 76,304)( 77,305)( 78,306)( 79,307)( 80,308)( 81,309)( 82,310)( 83,311)( 84,312)( 85,313)( 86,314)( 87,315)( 88,316)( 89,317)( 90,318)( 91,319)( 92,320)( 93,321)( 94,322)( 95,323)( 96,324)( 97,325)( 98,326)( 99,327)(100,328)(101,329)(102,330)(103,331)(104,332)(105,333)(106,334)(107,335)(108,336)(109,337)(110,338)(111,339)(112,340)(113,341)(114,342)(115,400)(116,401)(117,402)(118,403)(119,404)(120,405)(121,406)(122,407)(123,408)(124,409)(125,410)(126,411)(127,412)(128,413)(129,414)(130,415)(131,416)(132,417)(133,418)(134,419)(135,420)(136,421)(137,422)(138,423)(139,424)(140,425)(141,426)(142,427)(143,428)(144,429)(145,430)(146,431)(147,432)(148,433)(149,434)(150,435)(151,436)(152,437)(153,438)(154,439)(155,440)(156,441)(157,442)(158,443)(159,444)(160,445)(161,446)(162,447)(163,448)(164,449)(165,450)(166,451)(167,452)(168,453)(169,454)(170,455)(171,456)(172,343)(173,344)(174,345)(175,346)(176,347)(177,348)(178,349)(179,350)(180,351)(181,352)(182,353)(183,354)(184,355)(185,356)(186,357)(187,358)(188,359)(189,360)(190,361)(191,362)(192,363)(193,364)(194,365)(195,366)(196,367)(197,368)(198,369)(199,370)(200,371)(201,372)(202,373)(203,374)(204,375)(205,376)(206,377)(207,378)(208,379)(209,380)(210,381)(211,382)(212,383)(213,384)(214,385)(215,386)(216,387)(217,388)(218,389)(219,390)(220,391)(221,392)(222,393)(223,394)(224,395)(225,396)(226,397)(227,398)(228,399); poly := sub<Sym(456)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*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*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*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*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*s0*s1*s0*s1 >;
References
None.
to this polytope.