Overview
- Group
- SmallGroup(1632,1195)
- Rank
- 3
- Schläfli Type
- {102,6}
- Vertices, edges, …
- 136, 408, 8
- Order of s0s1s2
- 68
- 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
12-fold
17-fold
24-fold
34-fold
68-fold
204-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 := ( 3, 4)( 5, 65)( 6, 66)( 7, 68)( 8, 67)( 9, 61)( 10, 62)( 11, 64)( 12, 63)( 13, 57)( 14, 58)( 15, 60)( 16, 59)( 17, 53)( 18, 54)( 19, 56)( 20, 55)( 21, 49)( 22, 50)( 23, 52)( 24, 51)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 33, 37)( 34, 38)( 35, 40)( 36, 39)( 69,137)( 70,138)( 71,140)( 72,139)( 73,201)( 74,202)( 75,204)( 76,203)( 77,197)( 78,198)( 79,200)( 80,199)( 81,193)( 82,194)( 83,196)( 84,195)( 85,189)( 86,190)( 87,192)( 88,191)( 89,185)( 90,186)( 91,188)( 92,187)( 93,181)( 94,182)( 95,184)( 96,183)( 97,177)( 98,178)( 99,180)(100,179)(101,173)(102,174)(103,176)(104,175)(105,169)(106,170)(107,172)(108,171)(109,165)(110,166)(111,168)(112,167)(113,161)(114,162)(115,164)(116,163)(117,157)(118,158)(119,160)(120,159)(121,153)(122,154)(123,156)(124,155)(125,149)(126,150)(127,152)(128,151)(129,145)(130,146)(131,148)(132,147)(133,141)(134,142)(135,144)(136,143)(207,208)(209,269)(210,270)(211,272)(212,271)(213,265)(214,266)(215,268)(216,267)(217,261)(218,262)(219,264)(220,263)(221,257)(222,258)(223,260)(224,259)(225,253)(226,254)(227,256)(228,255)(229,249)(230,250)(231,252)(232,251)(233,245)(234,246)(235,248)(236,247)(237,241)(238,242)(239,244)(240,243)(273,341)(274,342)(275,344)(276,343)(277,405)(278,406)(279,408)(280,407)(281,401)(282,402)(283,404)(284,403)(285,397)(286,398)(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,381)(302,382)(303,384)(304,383)(305,377)(306,378)(307,380)(308,379)(309,373)(310,374)(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)(317,365)(318,366)(319,368)(320,367)(321,361)(322,362)(323,364)(324,363)(325,357)(326,358)(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)(334,350)(335,352)(336,351)(337,345)(338,346)(339,348)(340,347);; s1 := ( 1,277)( 2,280)( 3,279)( 4,278)( 5,273)( 6,276)( 7,275)( 8,274)( 9,337)( 10,340)( 11,339)( 12,338)( 13,333)( 14,336)( 15,335)( 16,334)( 17,329)( 18,332)( 19,331)( 20,330)( 21,325)( 22,328)( 23,327)( 24,326)( 25,321)( 26,324)( 27,323)( 28,322)( 29,317)( 30,320)( 31,319)( 32,318)( 33,313)( 34,316)( 35,315)( 36,314)( 37,309)( 38,312)( 39,311)( 40,310)( 41,305)( 42,308)( 43,307)( 44,306)( 45,301)( 46,304)( 47,303)( 48,302)( 49,297)( 50,300)( 51,299)( 52,298)( 53,293)( 54,296)( 55,295)( 56,294)( 57,289)( 58,292)( 59,291)( 60,290)( 61,285)( 62,288)( 63,287)( 64,286)( 65,281)( 66,284)( 67,283)( 68,282)( 69,209)( 70,212)( 71,211)( 72,210)( 73,205)( 74,208)( 75,207)( 76,206)( 77,269)( 78,272)( 79,271)( 80,270)( 81,265)( 82,268)( 83,267)( 84,266)( 85,261)( 86,264)( 87,263)( 88,262)( 89,257)( 90,260)( 91,259)( 92,258)( 93,253)( 94,256)( 95,255)( 96,254)( 97,249)( 98,252)( 99,251)(100,250)(101,245)(102,248)(103,247)(104,246)(105,241)(106,244)(107,243)(108,242)(109,237)(110,240)(111,239)(112,238)(113,233)(114,236)(115,235)(116,234)(117,229)(118,232)(119,231)(120,230)(121,225)(122,228)(123,227)(124,226)(125,221)(126,224)(127,223)(128,222)(129,217)(130,220)(131,219)(132,218)(133,213)(134,216)(135,215)(136,214)(137,345)(138,348)(139,347)(140,346)(141,341)(142,344)(143,343)(144,342)(145,405)(146,408)(147,407)(148,406)(149,401)(150,404)(151,403)(152,402)(153,397)(154,400)(155,399)(156,398)(157,393)(158,396)(159,395)(160,394)(161,389)(162,392)(163,391)(164,390)(165,385)(166,388)(167,387)(168,386)(169,381)(170,384)(171,383)(172,382)(173,377)(174,380)(175,379)(176,378)(177,373)(178,376)(179,375)(180,374)(181,369)(182,372)(183,371)(184,370)(185,365)(186,368)(187,367)(188,366)(189,361)(190,364)(191,363)(192,362)(193,357)(194,360)(195,359)(196,358)(197,353)(198,356)(199,355)(200,354)(201,349)(202,352)(203,351)(204,350);; s2 := ( 1, 2)( 5, 6)( 9, 10)( 13, 14)( 17, 18)( 21, 22)( 25, 26)( 29, 30)( 33, 34)( 37, 38)( 41, 42)( 45, 46)( 49, 50)( 53, 54)( 57, 58)( 61, 62)( 65, 66)( 69,138)( 70,137)( 71,139)( 72,140)( 73,142)( 74,141)( 75,143)( 76,144)( 77,146)( 78,145)( 79,147)( 80,148)( 81,150)( 82,149)( 83,151)( 84,152)( 85,154)( 86,153)( 87,155)( 88,156)( 89,158)( 90,157)( 91,159)( 92,160)( 93,162)( 94,161)( 95,163)( 96,164)( 97,166)( 98,165)( 99,167)(100,168)(101,170)(102,169)(103,171)(104,172)(105,174)(106,173)(107,175)(108,176)(109,178)(110,177)(111,179)(112,180)(113,182)(114,181)(115,183)(116,184)(117,186)(118,185)(119,187)(120,188)(121,190)(122,189)(123,191)(124,192)(125,194)(126,193)(127,195)(128,196)(129,198)(130,197)(131,199)(132,200)(133,202)(134,201)(135,203)(136,204)(205,206)(209,210)(213,214)(217,218)(221,222)(225,226)(229,230)(233,234)(237,238)(241,242)(245,246)(249,250)(253,254)(257,258)(261,262)(265,266)(269,270)(273,342)(274,341)(275,343)(276,344)(277,346)(278,345)(279,347)(280,348)(281,350)(282,349)(283,351)(284,352)(285,354)(286,353)(287,355)(288,356)(289,358)(290,357)(291,359)(292,360)(293,362)(294,361)(295,363)(296,364)(297,366)(298,365)(299,367)(300,368)(301,370)(302,369)(303,371)(304,372)(305,374)(306,373)(307,375)(308,376)(309,378)(310,377)(311,379)(312,380)(313,382)(314,381)(315,383)(316,384)(317,386)(318,385)(319,387)(320,388)(321,390)(322,389)(323,391)(324,392)(325,394)(326,393)(327,395)(328,396)(329,398)(330,397)(331,399)(332,400)(333,402)(334,401)(335,403)(336,404)(337,406)(338,405)(339,407)(340,408);; 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,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(408)!( 3, 4)( 5, 65)( 6, 66)( 7, 68)( 8, 67)( 9, 61)( 10, 62)( 11, 64)( 12, 63)( 13, 57)( 14, 58)( 15, 60)( 16, 59)( 17, 53)( 18, 54)( 19, 56)( 20, 55)( 21, 49)( 22, 50)( 23, 52)( 24, 51)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 33, 37)( 34, 38)( 35, 40)( 36, 39)( 69,137)( 70,138)( 71,140)( 72,139)( 73,201)( 74,202)( 75,204)( 76,203)( 77,197)( 78,198)( 79,200)( 80,199)( 81,193)( 82,194)( 83,196)( 84,195)( 85,189)( 86,190)( 87,192)( 88,191)( 89,185)( 90,186)( 91,188)( 92,187)( 93,181)( 94,182)( 95,184)( 96,183)( 97,177)( 98,178)( 99,180)(100,179)(101,173)(102,174)(103,176)(104,175)(105,169)(106,170)(107,172)(108,171)(109,165)(110,166)(111,168)(112,167)(113,161)(114,162)(115,164)(116,163)(117,157)(118,158)(119,160)(120,159)(121,153)(122,154)(123,156)(124,155)(125,149)(126,150)(127,152)(128,151)(129,145)(130,146)(131,148)(132,147)(133,141)(134,142)(135,144)(136,143)(207,208)(209,269)(210,270)(211,272)(212,271)(213,265)(214,266)(215,268)(216,267)(217,261)(218,262)(219,264)(220,263)(221,257)(222,258)(223,260)(224,259)(225,253)(226,254)(227,256)(228,255)(229,249)(230,250)(231,252)(232,251)(233,245)(234,246)(235,248)(236,247)(237,241)(238,242)(239,244)(240,243)(273,341)(274,342)(275,344)(276,343)(277,405)(278,406)(279,408)(280,407)(281,401)(282,402)(283,404)(284,403)(285,397)(286,398)(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,381)(302,382)(303,384)(304,383)(305,377)(306,378)(307,380)(308,379)(309,373)(310,374)(311,376)(312,375)(313,369)(314,370)(315,372)(316,371)(317,365)(318,366)(319,368)(320,367)(321,361)(322,362)(323,364)(324,363)(325,357)(326,358)(327,360)(328,359)(329,353)(330,354)(331,356)(332,355)(333,349)(334,350)(335,352)(336,351)(337,345)(338,346)(339,348)(340,347); s1 := Sym(408)!( 1,277)( 2,280)( 3,279)( 4,278)( 5,273)( 6,276)( 7,275)( 8,274)( 9,337)( 10,340)( 11,339)( 12,338)( 13,333)( 14,336)( 15,335)( 16,334)( 17,329)( 18,332)( 19,331)( 20,330)( 21,325)( 22,328)( 23,327)( 24,326)( 25,321)( 26,324)( 27,323)( 28,322)( 29,317)( 30,320)( 31,319)( 32,318)( 33,313)( 34,316)( 35,315)( 36,314)( 37,309)( 38,312)( 39,311)( 40,310)( 41,305)( 42,308)( 43,307)( 44,306)( 45,301)( 46,304)( 47,303)( 48,302)( 49,297)( 50,300)( 51,299)( 52,298)( 53,293)( 54,296)( 55,295)( 56,294)( 57,289)( 58,292)( 59,291)( 60,290)( 61,285)( 62,288)( 63,287)( 64,286)( 65,281)( 66,284)( 67,283)( 68,282)( 69,209)( 70,212)( 71,211)( 72,210)( 73,205)( 74,208)( 75,207)( 76,206)( 77,269)( 78,272)( 79,271)( 80,270)( 81,265)( 82,268)( 83,267)( 84,266)( 85,261)( 86,264)( 87,263)( 88,262)( 89,257)( 90,260)( 91,259)( 92,258)( 93,253)( 94,256)( 95,255)( 96,254)( 97,249)( 98,252)( 99,251)(100,250)(101,245)(102,248)(103,247)(104,246)(105,241)(106,244)(107,243)(108,242)(109,237)(110,240)(111,239)(112,238)(113,233)(114,236)(115,235)(116,234)(117,229)(118,232)(119,231)(120,230)(121,225)(122,228)(123,227)(124,226)(125,221)(126,224)(127,223)(128,222)(129,217)(130,220)(131,219)(132,218)(133,213)(134,216)(135,215)(136,214)(137,345)(138,348)(139,347)(140,346)(141,341)(142,344)(143,343)(144,342)(145,405)(146,408)(147,407)(148,406)(149,401)(150,404)(151,403)(152,402)(153,397)(154,400)(155,399)(156,398)(157,393)(158,396)(159,395)(160,394)(161,389)(162,392)(163,391)(164,390)(165,385)(166,388)(167,387)(168,386)(169,381)(170,384)(171,383)(172,382)(173,377)(174,380)(175,379)(176,378)(177,373)(178,376)(179,375)(180,374)(181,369)(182,372)(183,371)(184,370)(185,365)(186,368)(187,367)(188,366)(189,361)(190,364)(191,363)(192,362)(193,357)(194,360)(195,359)(196,358)(197,353)(198,356)(199,355)(200,354)(201,349)(202,352)(203,351)(204,350); s2 := Sym(408)!( 1, 2)( 5, 6)( 9, 10)( 13, 14)( 17, 18)( 21, 22)( 25, 26)( 29, 30)( 33, 34)( 37, 38)( 41, 42)( 45, 46)( 49, 50)( 53, 54)( 57, 58)( 61, 62)( 65, 66)( 69,138)( 70,137)( 71,139)( 72,140)( 73,142)( 74,141)( 75,143)( 76,144)( 77,146)( 78,145)( 79,147)( 80,148)( 81,150)( 82,149)( 83,151)( 84,152)( 85,154)( 86,153)( 87,155)( 88,156)( 89,158)( 90,157)( 91,159)( 92,160)( 93,162)( 94,161)( 95,163)( 96,164)( 97,166)( 98,165)( 99,167)(100,168)(101,170)(102,169)(103,171)(104,172)(105,174)(106,173)(107,175)(108,176)(109,178)(110,177)(111,179)(112,180)(113,182)(114,181)(115,183)(116,184)(117,186)(118,185)(119,187)(120,188)(121,190)(122,189)(123,191)(124,192)(125,194)(126,193)(127,195)(128,196)(129,198)(130,197)(131,199)(132,200)(133,202)(134,201)(135,203)(136,204)(205,206)(209,210)(213,214)(217,218)(221,222)(225,226)(229,230)(233,234)(237,238)(241,242)(245,246)(249,250)(253,254)(257,258)(261,262)(265,266)(269,270)(273,342)(274,341)(275,343)(276,344)(277,346)(278,345)(279,347)(280,348)(281,350)(282,349)(283,351)(284,352)(285,354)(286,353)(287,355)(288,356)(289,358)(290,357)(291,359)(292,360)(293,362)(294,361)(295,363)(296,364)(297,366)(298,365)(299,367)(300,368)(301,370)(302,369)(303,371)(304,372)(305,374)(306,373)(307,375)(308,376)(309,378)(310,377)(311,379)(312,380)(313,382)(314,381)(315,383)(316,384)(317,386)(318,385)(319,387)(320,388)(321,390)(322,389)(323,391)(324,392)(325,394)(326,393)(327,395)(328,396)(329,398)(330,397)(331,399)(332,400)(333,402)(334,401)(335,403)(336,404)(337,406)(338,405)(339,407)(340,408); poly := sub<Sym(408)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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.