Overview
- Group
- SmallGroup(1560,208)
- Rank
- 3
- Schläfli Type
- {78,10}
- Vertices, edges, …
- 78, 390, 10
- Order of s0s1s2
- 390
- Order of s0s1s2s1
- 2
- Also known as
- {78,10|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
10-fold
13-fold
15-fold
30-fold
39-fold
65-fold
78-fold
130-fold
195-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, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 66,131)( 67,143)( 68,142)( 69,141)( 70,140)( 71,139)( 72,138)( 73,137)( 74,136)( 75,135)( 76,134)( 77,133)( 78,132)( 79,144)( 80,156)( 81,155)( 82,154)( 83,153)( 84,152)( 85,151)( 86,150)( 87,149)( 88,148)( 89,147)( 90,146)( 91,145)( 92,157)( 93,169)( 94,168)( 95,167)( 96,166)( 97,165)( 98,164)( 99,163)(100,162)(101,161)(102,160)(103,159)(104,158)(105,170)(106,182)(107,181)(108,180)(109,179)(110,178)(111,177)(112,176)(113,175)(114,174)(115,173)(116,172)(117,171)(118,183)(119,195)(120,194)(121,193)(122,192)(123,191)(124,190)(125,189)(126,188)(127,187)(128,186)(129,185)(130,184)(197,208)(198,207)(199,206)(200,205)(201,204)(202,203)(210,221)(211,220)(212,219)(213,218)(214,217)(215,216)(223,234)(224,233)(225,232)(226,231)(227,230)(228,229)(236,247)(237,246)(238,245)(239,244)(240,243)(241,242)(249,260)(250,259)(251,258)(252,257)(253,256)(254,255)(261,326)(262,338)(263,337)(264,336)(265,335)(266,334)(267,333)(268,332)(269,331)(270,330)(271,329)(272,328)(273,327)(274,339)(275,351)(276,350)(277,349)(278,348)(279,347)(280,346)(281,345)(282,344)(283,343)(284,342)(285,341)(286,340)(287,352)(288,364)(289,363)(290,362)(291,361)(292,360)(293,359)(294,358)(295,357)(296,356)(297,355)(298,354)(299,353)(300,365)(301,377)(302,376)(303,375)(304,374)(305,373)(306,372)(307,371)(308,370)(309,369)(310,368)(311,367)(312,366)(313,378)(314,390)(315,389)(316,388)(317,387)(318,386)(319,385)(320,384)(321,383)(322,382)(323,381)(324,380)(325,379);; s1 := ( 1, 67)( 2, 66)( 3, 78)( 4, 77)( 5, 76)( 6, 75)( 7, 74)( 8, 73)( 9, 72)( 10, 71)( 11, 70)( 12, 69)( 13, 68)( 14,119)( 15,118)( 16,130)( 17,129)( 18,128)( 19,127)( 20,126)( 21,125)( 22,124)( 23,123)( 24,122)( 25,121)( 26,120)( 27,106)( 28,105)( 29,117)( 30,116)( 31,115)( 32,114)( 33,113)( 34,112)( 35,111)( 36,110)( 37,109)( 38,108)( 39,107)( 40, 93)( 41, 92)( 42,104)( 43,103)( 44,102)( 45,101)( 46,100)( 47, 99)( 48, 98)( 49, 97)( 50, 96)( 51, 95)( 52, 94)( 53, 80)( 54, 79)( 55, 91)( 56, 90)( 57, 89)( 58, 88)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 83)( 64, 82)( 65, 81)(131,132)(133,143)(134,142)(135,141)(136,140)(137,139)(144,184)(145,183)(146,195)(147,194)(148,193)(149,192)(150,191)(151,190)(152,189)(153,188)(154,187)(155,186)(156,185)(157,171)(158,170)(159,182)(160,181)(161,180)(162,179)(163,178)(164,177)(165,176)(166,175)(167,174)(168,173)(169,172)(196,262)(197,261)(198,273)(199,272)(200,271)(201,270)(202,269)(203,268)(204,267)(205,266)(206,265)(207,264)(208,263)(209,314)(210,313)(211,325)(212,324)(213,323)(214,322)(215,321)(216,320)(217,319)(218,318)(219,317)(220,316)(221,315)(222,301)(223,300)(224,312)(225,311)(226,310)(227,309)(228,308)(229,307)(230,306)(231,305)(232,304)(233,303)(234,302)(235,288)(236,287)(237,299)(238,298)(239,297)(240,296)(241,295)(242,294)(243,293)(244,292)(245,291)(246,290)(247,289)(248,275)(249,274)(250,286)(251,285)(252,284)(253,283)(254,282)(255,281)(256,280)(257,279)(258,278)(259,277)(260,276)(326,327)(328,338)(329,337)(330,336)(331,335)(332,334)(339,379)(340,378)(341,390)(342,389)(343,388)(344,387)(345,386)(346,385)(347,384)(348,383)(349,382)(350,381)(351,380)(352,366)(353,365)(354,377)(355,376)(356,375)(357,374)(358,373)(359,372)(360,371)(361,370)(362,369)(363,368)(364,367);; s2 := ( 1,209)( 2,210)( 3,211)( 4,212)( 5,213)( 6,214)( 7,215)( 8,216)( 9,217)( 10,218)( 11,219)( 12,220)( 13,221)( 14,196)( 15,197)( 16,198)( 17,199)( 18,200)( 19,201)( 20,202)( 21,203)( 22,204)( 23,205)( 24,206)( 25,207)( 26,208)( 27,248)( 28,249)( 29,250)( 30,251)( 31,252)( 32,253)( 33,254)( 34,255)( 35,256)( 36,257)( 37,258)( 38,259)( 39,260)( 40,235)( 41,236)( 42,237)( 43,238)( 44,239)( 45,240)( 46,241)( 47,242)( 48,243)( 49,244)( 50,245)( 51,246)( 52,247)( 53,222)( 54,223)( 55,224)( 56,225)( 57,226)( 58,227)( 59,228)( 60,229)( 61,230)( 62,231)( 63,232)( 64,233)( 65,234)( 66,274)( 67,275)( 68,276)( 69,277)( 70,278)( 71,279)( 72,280)( 73,281)( 74,282)( 75,283)( 76,284)( 77,285)( 78,286)( 79,261)( 80,262)( 81,263)( 82,264)( 83,265)( 84,266)( 85,267)( 86,268)( 87,269)( 88,270)( 89,271)( 90,272)( 91,273)( 92,313)( 93,314)( 94,315)( 95,316)( 96,317)( 97,318)( 98,319)( 99,320)(100,321)(101,322)(102,323)(103,324)(104,325)(105,300)(106,301)(107,302)(108,303)(109,304)(110,305)(111,306)(112,307)(113,308)(114,309)(115,310)(116,311)(117,312)(118,287)(119,288)(120,289)(121,290)(122,291)(123,292)(124,293)(125,294)(126,295)(127,296)(128,297)(129,298)(130,299)(131,339)(132,340)(133,341)(134,342)(135,343)(136,344)(137,345)(138,346)(139,347)(140,348)(141,349)(142,350)(143,351)(144,326)(145,327)(146,328)(147,329)(148,330)(149,331)(150,332)(151,333)(152,334)(153,335)(154,336)(155,337)(156,338)(157,378)(158,379)(159,380)(160,381)(161,382)(162,383)(163,384)(164,385)(165,386)(166,387)(167,388)(168,389)(169,390)(170,365)(171,366)(172,367)(173,368)(174,369)(175,370)(176,371)(177,372)(178,373)(179,374)(180,375)(181,376)(182,377)(183,352)(184,353)(185,354)(186,355)(187,356)(188,357)(189,358)(190,359)(191,360)(192,361)(193,362)(194,363)(195,364);; 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*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(390)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 66,131)( 67,143)( 68,142)( 69,141)( 70,140)( 71,139)( 72,138)( 73,137)( 74,136)( 75,135)( 76,134)( 77,133)( 78,132)( 79,144)( 80,156)( 81,155)( 82,154)( 83,153)( 84,152)( 85,151)( 86,150)( 87,149)( 88,148)( 89,147)( 90,146)( 91,145)( 92,157)( 93,169)( 94,168)( 95,167)( 96,166)( 97,165)( 98,164)( 99,163)(100,162)(101,161)(102,160)(103,159)(104,158)(105,170)(106,182)(107,181)(108,180)(109,179)(110,178)(111,177)(112,176)(113,175)(114,174)(115,173)(116,172)(117,171)(118,183)(119,195)(120,194)(121,193)(122,192)(123,191)(124,190)(125,189)(126,188)(127,187)(128,186)(129,185)(130,184)(197,208)(198,207)(199,206)(200,205)(201,204)(202,203)(210,221)(211,220)(212,219)(213,218)(214,217)(215,216)(223,234)(224,233)(225,232)(226,231)(227,230)(228,229)(236,247)(237,246)(238,245)(239,244)(240,243)(241,242)(249,260)(250,259)(251,258)(252,257)(253,256)(254,255)(261,326)(262,338)(263,337)(264,336)(265,335)(266,334)(267,333)(268,332)(269,331)(270,330)(271,329)(272,328)(273,327)(274,339)(275,351)(276,350)(277,349)(278,348)(279,347)(280,346)(281,345)(282,344)(283,343)(284,342)(285,341)(286,340)(287,352)(288,364)(289,363)(290,362)(291,361)(292,360)(293,359)(294,358)(295,357)(296,356)(297,355)(298,354)(299,353)(300,365)(301,377)(302,376)(303,375)(304,374)(305,373)(306,372)(307,371)(308,370)(309,369)(310,368)(311,367)(312,366)(313,378)(314,390)(315,389)(316,388)(317,387)(318,386)(319,385)(320,384)(321,383)(322,382)(323,381)(324,380)(325,379); s1 := Sym(390)!( 1, 67)( 2, 66)( 3, 78)( 4, 77)( 5, 76)( 6, 75)( 7, 74)( 8, 73)( 9, 72)( 10, 71)( 11, 70)( 12, 69)( 13, 68)( 14,119)( 15,118)( 16,130)( 17,129)( 18,128)( 19,127)( 20,126)( 21,125)( 22,124)( 23,123)( 24,122)( 25,121)( 26,120)( 27,106)( 28,105)( 29,117)( 30,116)( 31,115)( 32,114)( 33,113)( 34,112)( 35,111)( 36,110)( 37,109)( 38,108)( 39,107)( 40, 93)( 41, 92)( 42,104)( 43,103)( 44,102)( 45,101)( 46,100)( 47, 99)( 48, 98)( 49, 97)( 50, 96)( 51, 95)( 52, 94)( 53, 80)( 54, 79)( 55, 91)( 56, 90)( 57, 89)( 58, 88)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 83)( 64, 82)( 65, 81)(131,132)(133,143)(134,142)(135,141)(136,140)(137,139)(144,184)(145,183)(146,195)(147,194)(148,193)(149,192)(150,191)(151,190)(152,189)(153,188)(154,187)(155,186)(156,185)(157,171)(158,170)(159,182)(160,181)(161,180)(162,179)(163,178)(164,177)(165,176)(166,175)(167,174)(168,173)(169,172)(196,262)(197,261)(198,273)(199,272)(200,271)(201,270)(202,269)(203,268)(204,267)(205,266)(206,265)(207,264)(208,263)(209,314)(210,313)(211,325)(212,324)(213,323)(214,322)(215,321)(216,320)(217,319)(218,318)(219,317)(220,316)(221,315)(222,301)(223,300)(224,312)(225,311)(226,310)(227,309)(228,308)(229,307)(230,306)(231,305)(232,304)(233,303)(234,302)(235,288)(236,287)(237,299)(238,298)(239,297)(240,296)(241,295)(242,294)(243,293)(244,292)(245,291)(246,290)(247,289)(248,275)(249,274)(250,286)(251,285)(252,284)(253,283)(254,282)(255,281)(256,280)(257,279)(258,278)(259,277)(260,276)(326,327)(328,338)(329,337)(330,336)(331,335)(332,334)(339,379)(340,378)(341,390)(342,389)(343,388)(344,387)(345,386)(346,385)(347,384)(348,383)(349,382)(350,381)(351,380)(352,366)(353,365)(354,377)(355,376)(356,375)(357,374)(358,373)(359,372)(360,371)(361,370)(362,369)(363,368)(364,367); s2 := Sym(390)!( 1,209)( 2,210)( 3,211)( 4,212)( 5,213)( 6,214)( 7,215)( 8,216)( 9,217)( 10,218)( 11,219)( 12,220)( 13,221)( 14,196)( 15,197)( 16,198)( 17,199)( 18,200)( 19,201)( 20,202)( 21,203)( 22,204)( 23,205)( 24,206)( 25,207)( 26,208)( 27,248)( 28,249)( 29,250)( 30,251)( 31,252)( 32,253)( 33,254)( 34,255)( 35,256)( 36,257)( 37,258)( 38,259)( 39,260)( 40,235)( 41,236)( 42,237)( 43,238)( 44,239)( 45,240)( 46,241)( 47,242)( 48,243)( 49,244)( 50,245)( 51,246)( 52,247)( 53,222)( 54,223)( 55,224)( 56,225)( 57,226)( 58,227)( 59,228)( 60,229)( 61,230)( 62,231)( 63,232)( 64,233)( 65,234)( 66,274)( 67,275)( 68,276)( 69,277)( 70,278)( 71,279)( 72,280)( 73,281)( 74,282)( 75,283)( 76,284)( 77,285)( 78,286)( 79,261)( 80,262)( 81,263)( 82,264)( 83,265)( 84,266)( 85,267)( 86,268)( 87,269)( 88,270)( 89,271)( 90,272)( 91,273)( 92,313)( 93,314)( 94,315)( 95,316)( 96,317)( 97,318)( 98,319)( 99,320)(100,321)(101,322)(102,323)(103,324)(104,325)(105,300)(106,301)(107,302)(108,303)(109,304)(110,305)(111,306)(112,307)(113,308)(114,309)(115,310)(116,311)(117,312)(118,287)(119,288)(120,289)(121,290)(122,291)(123,292)(124,293)(125,294)(126,295)(127,296)(128,297)(129,298)(130,299)(131,339)(132,340)(133,341)(134,342)(135,343)(136,344)(137,345)(138,346)(139,347)(140,348)(141,349)(142,350)(143,351)(144,326)(145,327)(146,328)(147,329)(148,330)(149,331)(150,332)(151,333)(152,334)(153,335)(154,336)(155,337)(156,338)(157,378)(158,379)(159,380)(160,381)(161,382)(162,383)(163,384)(164,385)(165,386)(166,387)(167,388)(168,389)(169,390)(170,365)(171,366)(172,367)(173,368)(174,369)(175,370)(176,371)(177,372)(178,373)(179,374)(180,375)(181,376)(182,377)(183,352)(184,353)(185,354)(186,355)(187,356)(188,357)(189,358)(190,359)(191,360)(192,361)(193,362)(194,363)(195,364); poly := sub<Sym(390)|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*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 >;
References
None.
to this polytope.