Overview
- Group
- SmallGroup(1512,561)
- Rank
- 3
- Schläfli Type
- {42,6}
- Vertices, edges, …
- 126, 378, 18
- Order of s0s1s2
- 42
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
7-fold
9-fold
14-fold
18-fold
21-fold
27-fold
42-fold
54-fold
63-fold
126-fold
189-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := ( 4, 19)( 5, 20)( 6, 21)( 7, 16)( 8, 17)( 9, 18)( 10, 13)( 11, 14)( 12, 15)( 22, 43)( 23, 44)( 24, 45)( 25, 61)( 26, 62)( 27, 63)( 28, 58)( 29, 59)( 30, 60)( 31, 55)( 32, 56)( 33, 57)( 34, 52)( 35, 53)( 36, 54)( 37, 49)( 38, 50)( 39, 51)( 40, 46)( 41, 47)( 42, 48)( 64,127)( 65,128)( 66,129)( 67,145)( 68,146)( 69,147)( 70,142)( 71,143)( 72,144)( 73,139)( 74,140)( 75,141)( 76,136)( 77,137)( 78,138)( 79,133)( 80,134)( 81,135)( 82,130)( 83,131)( 84,132)( 85,169)( 86,170)( 87,171)( 88,187)( 89,188)( 90,189)( 91,184)( 92,185)( 93,186)( 94,181)( 95,182)( 96,183)( 97,178)( 98,179)( 99,180)(100,175)(101,176)(102,177)(103,172)(104,173)(105,174)(106,148)(107,149)(108,150)(109,166)(110,167)(111,168)(112,163)(113,164)(114,165)(115,160)(116,161)(117,162)(118,157)(119,158)(120,159)(121,154)(122,155)(123,156)(124,151)(125,152)(126,153)(193,208)(194,209)(195,210)(196,205)(197,206)(198,207)(199,202)(200,203)(201,204)(211,232)(212,233)(213,234)(214,250)(215,251)(216,252)(217,247)(218,248)(219,249)(220,244)(221,245)(222,246)(223,241)(224,242)(225,243)(226,238)(227,239)(228,240)(229,235)(230,236)(231,237)(253,316)(254,317)(255,318)(256,334)(257,335)(258,336)(259,331)(260,332)(261,333)(262,328)(263,329)(264,330)(265,325)(266,326)(267,327)(268,322)(269,323)(270,324)(271,319)(272,320)(273,321)(274,358)(275,359)(276,360)(277,376)(278,377)(279,378)(280,373)(281,374)(282,375)(283,370)(284,371)(285,372)(286,367)(287,368)(288,369)(289,364)(290,365)(291,366)(292,361)(293,362)(294,363)(295,337)(296,338)(297,339)(298,355)(299,356)(300,357)(301,352)(302,353)(303,354)(304,349)(305,350)(306,351)(307,346)(308,347)(309,348)(310,343)(311,344)(312,345)(313,340)(314,341)(315,342);; s1 := ( 1,341)( 2,342)( 3,340)( 4,338)( 5,339)( 6,337)( 7,356)( 8,357)( 9,355)( 10,353)( 11,354)( 12,352)( 13,350)( 14,351)( 15,349)( 16,347)( 17,348)( 18,346)( 19,344)( 20,345)( 21,343)( 22,321)( 23,319)( 24,320)( 25,318)( 26,316)( 27,317)( 28,336)( 29,334)( 30,335)( 31,333)( 32,331)( 33,332)( 34,330)( 35,328)( 36,329)( 37,327)( 38,325)( 39,326)( 40,324)( 41,322)( 42,323)( 43,361)( 44,362)( 45,363)( 46,358)( 47,359)( 48,360)( 49,376)( 50,377)( 51,378)( 52,373)( 53,374)( 54,375)( 55,370)( 56,371)( 57,372)( 58,367)( 59,368)( 60,369)( 61,364)( 62,365)( 63,366)( 64,278)( 65,279)( 66,277)( 67,275)( 68,276)( 69,274)( 70,293)( 71,294)( 72,292)( 73,290)( 74,291)( 75,289)( 76,287)( 77,288)( 78,286)( 79,284)( 80,285)( 81,283)( 82,281)( 83,282)( 84,280)( 85,258)( 86,256)( 87,257)( 88,255)( 89,253)( 90,254)( 91,273)( 92,271)( 93,272)( 94,270)( 95,268)( 96,269)( 97,267)( 98,265)( 99,266)(100,264)(101,262)(102,263)(103,261)(104,259)(105,260)(106,298)(107,299)(108,300)(109,295)(110,296)(111,297)(112,313)(113,314)(114,315)(115,310)(116,311)(117,312)(118,307)(119,308)(120,309)(121,304)(122,305)(123,306)(124,301)(125,302)(126,303)(127,215)(128,216)(129,214)(130,212)(131,213)(132,211)(133,230)(134,231)(135,229)(136,227)(137,228)(138,226)(139,224)(140,225)(141,223)(142,221)(143,222)(144,220)(145,218)(146,219)(147,217)(148,195)(149,193)(150,194)(151,192)(152,190)(153,191)(154,210)(155,208)(156,209)(157,207)(158,205)(159,206)(160,204)(161,202)(162,203)(163,201)(164,199)(165,200)(166,198)(167,196)(168,197)(169,235)(170,236)(171,237)(172,232)(173,233)(174,234)(175,250)(176,251)(177,252)(178,247)(179,248)(180,249)(181,244)(182,245)(183,246)(184,241)(185,242)(186,243)(187,238)(188,239)(189,240);; s2 := ( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 64,127)( 65,129)( 66,128)( 67,130)( 68,132)( 69,131)( 70,133)( 71,135)( 72,134)( 73,136)( 74,138)( 75,137)( 76,139)( 77,141)( 78,140)( 79,142)( 80,144)( 81,143)( 82,145)( 83,147)( 84,146)( 85,148)( 86,150)( 87,149)( 88,151)( 89,153)( 90,152)( 91,154)( 92,156)( 93,155)( 94,157)( 95,159)( 96,158)( 97,160)( 98,162)( 99,161)(100,163)(101,165)(102,164)(103,166)(104,168)(105,167)(106,169)(107,171)(108,170)(109,172)(110,174)(111,173)(112,175)(113,177)(114,176)(115,178)(116,180)(117,179)(118,181)(119,183)(120,182)(121,184)(122,186)(123,185)(124,187)(125,189)(126,188)(191,192)(194,195)(197,198)(200,201)(203,204)(206,207)(209,210)(212,213)(215,216)(218,219)(221,222)(224,225)(227,228)(230,231)(233,234)(236,237)(239,240)(242,243)(245,246)(248,249)(251,252)(253,316)(254,318)(255,317)(256,319)(257,321)(258,320)(259,322)(260,324)(261,323)(262,325)(263,327)(264,326)(265,328)(266,330)(267,329)(268,331)(269,333)(270,332)(271,334)(272,336)(273,335)(274,337)(275,339)(276,338)(277,340)(278,342)(279,341)(280,343)(281,345)(282,344)(283,346)(284,348)(285,347)(286,349)(287,351)(288,350)(289,352)(290,354)(291,353)(292,355)(293,357)(294,356)(295,358)(296,360)(297,359)(298,361)(299,363)(300,362)(301,364)(302,366)(303,365)(304,367)(305,369)(306,368)(307,370)(308,372)(309,371)(310,373)(311,375)(312,374)(313,376)(314,378)(315,377);; 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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0,
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(378)!( 4, 19)( 5, 20)( 6, 21)( 7, 16)( 8, 17)( 9, 18)( 10, 13)( 11, 14)( 12, 15)( 22, 43)( 23, 44)( 24, 45)( 25, 61)( 26, 62)( 27, 63)( 28, 58)( 29, 59)( 30, 60)( 31, 55)( 32, 56)( 33, 57)( 34, 52)( 35, 53)( 36, 54)( 37, 49)( 38, 50)( 39, 51)( 40, 46)( 41, 47)( 42, 48)( 64,127)( 65,128)( 66,129)( 67,145)( 68,146)( 69,147)( 70,142)( 71,143)( 72,144)( 73,139)( 74,140)( 75,141)( 76,136)( 77,137)( 78,138)( 79,133)( 80,134)( 81,135)( 82,130)( 83,131)( 84,132)( 85,169)( 86,170)( 87,171)( 88,187)( 89,188)( 90,189)( 91,184)( 92,185)( 93,186)( 94,181)( 95,182)( 96,183)( 97,178)( 98,179)( 99,180)(100,175)(101,176)(102,177)(103,172)(104,173)(105,174)(106,148)(107,149)(108,150)(109,166)(110,167)(111,168)(112,163)(113,164)(114,165)(115,160)(116,161)(117,162)(118,157)(119,158)(120,159)(121,154)(122,155)(123,156)(124,151)(125,152)(126,153)(193,208)(194,209)(195,210)(196,205)(197,206)(198,207)(199,202)(200,203)(201,204)(211,232)(212,233)(213,234)(214,250)(215,251)(216,252)(217,247)(218,248)(219,249)(220,244)(221,245)(222,246)(223,241)(224,242)(225,243)(226,238)(227,239)(228,240)(229,235)(230,236)(231,237)(253,316)(254,317)(255,318)(256,334)(257,335)(258,336)(259,331)(260,332)(261,333)(262,328)(263,329)(264,330)(265,325)(266,326)(267,327)(268,322)(269,323)(270,324)(271,319)(272,320)(273,321)(274,358)(275,359)(276,360)(277,376)(278,377)(279,378)(280,373)(281,374)(282,375)(283,370)(284,371)(285,372)(286,367)(287,368)(288,369)(289,364)(290,365)(291,366)(292,361)(293,362)(294,363)(295,337)(296,338)(297,339)(298,355)(299,356)(300,357)(301,352)(302,353)(303,354)(304,349)(305,350)(306,351)(307,346)(308,347)(309,348)(310,343)(311,344)(312,345)(313,340)(314,341)(315,342); s1 := Sym(378)!( 1,341)( 2,342)( 3,340)( 4,338)( 5,339)( 6,337)( 7,356)( 8,357)( 9,355)( 10,353)( 11,354)( 12,352)( 13,350)( 14,351)( 15,349)( 16,347)( 17,348)( 18,346)( 19,344)( 20,345)( 21,343)( 22,321)( 23,319)( 24,320)( 25,318)( 26,316)( 27,317)( 28,336)( 29,334)( 30,335)( 31,333)( 32,331)( 33,332)( 34,330)( 35,328)( 36,329)( 37,327)( 38,325)( 39,326)( 40,324)( 41,322)( 42,323)( 43,361)( 44,362)( 45,363)( 46,358)( 47,359)( 48,360)( 49,376)( 50,377)( 51,378)( 52,373)( 53,374)( 54,375)( 55,370)( 56,371)( 57,372)( 58,367)( 59,368)( 60,369)( 61,364)( 62,365)( 63,366)( 64,278)( 65,279)( 66,277)( 67,275)( 68,276)( 69,274)( 70,293)( 71,294)( 72,292)( 73,290)( 74,291)( 75,289)( 76,287)( 77,288)( 78,286)( 79,284)( 80,285)( 81,283)( 82,281)( 83,282)( 84,280)( 85,258)( 86,256)( 87,257)( 88,255)( 89,253)( 90,254)( 91,273)( 92,271)( 93,272)( 94,270)( 95,268)( 96,269)( 97,267)( 98,265)( 99,266)(100,264)(101,262)(102,263)(103,261)(104,259)(105,260)(106,298)(107,299)(108,300)(109,295)(110,296)(111,297)(112,313)(113,314)(114,315)(115,310)(116,311)(117,312)(118,307)(119,308)(120,309)(121,304)(122,305)(123,306)(124,301)(125,302)(126,303)(127,215)(128,216)(129,214)(130,212)(131,213)(132,211)(133,230)(134,231)(135,229)(136,227)(137,228)(138,226)(139,224)(140,225)(141,223)(142,221)(143,222)(144,220)(145,218)(146,219)(147,217)(148,195)(149,193)(150,194)(151,192)(152,190)(153,191)(154,210)(155,208)(156,209)(157,207)(158,205)(159,206)(160,204)(161,202)(162,203)(163,201)(164,199)(165,200)(166,198)(167,196)(168,197)(169,235)(170,236)(171,237)(172,232)(173,233)(174,234)(175,250)(176,251)(177,252)(178,247)(179,248)(180,249)(181,244)(182,245)(183,246)(184,241)(185,242)(186,243)(187,238)(188,239)(189,240); s2 := Sym(378)!( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 35, 36)( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 50, 51)( 53, 54)( 56, 57)( 59, 60)( 62, 63)( 64,127)( 65,129)( 66,128)( 67,130)( 68,132)( 69,131)( 70,133)( 71,135)( 72,134)( 73,136)( 74,138)( 75,137)( 76,139)( 77,141)( 78,140)( 79,142)( 80,144)( 81,143)( 82,145)( 83,147)( 84,146)( 85,148)( 86,150)( 87,149)( 88,151)( 89,153)( 90,152)( 91,154)( 92,156)( 93,155)( 94,157)( 95,159)( 96,158)( 97,160)( 98,162)( 99,161)(100,163)(101,165)(102,164)(103,166)(104,168)(105,167)(106,169)(107,171)(108,170)(109,172)(110,174)(111,173)(112,175)(113,177)(114,176)(115,178)(116,180)(117,179)(118,181)(119,183)(120,182)(121,184)(122,186)(123,185)(124,187)(125,189)(126,188)(191,192)(194,195)(197,198)(200,201)(203,204)(206,207)(209,210)(212,213)(215,216)(218,219)(221,222)(224,225)(227,228)(230,231)(233,234)(236,237)(239,240)(242,243)(245,246)(248,249)(251,252)(253,316)(254,318)(255,317)(256,319)(257,321)(258,320)(259,322)(260,324)(261,323)(262,325)(263,327)(264,326)(265,328)(266,330)(267,329)(268,331)(269,333)(270,332)(271,334)(272,336)(273,335)(274,337)(275,339)(276,338)(277,340)(278,342)(279,341)(280,343)(281,345)(282,344)(283,346)(284,348)(285,347)(286,349)(287,351)(288,350)(289,352)(290,354)(291,353)(292,355)(293,357)(294,356)(295,358)(296,360)(297,359)(298,361)(299,363)(300,362)(301,364)(302,366)(303,365)(304,367)(305,369)(306,368)(307,370)(308,372)(309,371)(310,373)(311,375)(312,374)(313,376)(314,378)(315,377); poly := sub<Sym(378)|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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s0, 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.