Overview
- Group
- SmallGroup(1620,130)
- Rank
- 3
- Schläfli Type
- {45,18}
- Vertices, edges, …
- 45, 405, 18
- Order of s0s1s2
- 90
- Order of s0s1s2s1
- 18
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
9-fold
15-fold
27-fold
45-fold
81-fold
135-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, 3)( 4, 7)( 5, 9)( 6, 8)( 10, 37)( 11, 39)( 12, 38)( 13, 43)( 14, 45)( 15, 44)( 16, 40)( 17, 42)( 18, 41)( 19, 28)( 20, 30)( 21, 29)( 22, 34)( 23, 36)( 24, 35)( 25, 31)( 26, 33)( 27, 32)( 46, 92)( 47, 91)( 48, 93)( 49, 98)( 50, 97)( 51, 99)( 52, 95)( 53, 94)( 54, 96)( 55,128)( 56,127)( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,119)( 65,118)( 66,120)( 67,125)( 68,124)( 69,126)( 70,122)( 71,121)( 72,123)( 73,110)( 74,109)( 75,111)( 76,116)( 77,115)( 78,117)( 79,113)( 80,112)( 81,114)( 82,101)( 83,100)( 84,102)( 85,107)( 86,106)( 87,108)( 88,104)( 89,103)( 90,105)(136,274)(137,276)(138,275)(139,271)(140,273)(141,272)(142,277)(143,279)(144,278)(145,310)(146,312)(147,311)(148,307)(149,309)(150,308)(151,313)(152,315)(153,314)(154,301)(155,303)(156,302)(157,298)(158,300)(159,299)(160,304)(161,306)(162,305)(163,292)(164,294)(165,293)(166,289)(167,291)(168,290)(169,295)(170,297)(171,296)(172,283)(173,285)(174,284)(175,280)(176,282)(177,281)(178,286)(179,288)(180,287)(181,365)(182,364)(183,366)(184,362)(185,361)(186,363)(187,368)(188,367)(189,369)(190,401)(191,400)(192,402)(193,398)(194,397)(195,399)(196,404)(197,403)(198,405)(199,392)(200,391)(201,393)(202,389)(203,388)(204,390)(205,395)(206,394)(207,396)(208,383)(209,382)(210,384)(211,380)(212,379)(213,381)(214,386)(215,385)(216,387)(217,374)(218,373)(219,375)(220,371)(221,370)(222,372)(223,377)(224,376)(225,378)(226,320)(227,319)(228,321)(229,317)(230,316)(231,318)(232,323)(233,322)(234,324)(235,356)(236,355)(237,357)(238,353)(239,352)(240,354)(241,359)(242,358)(243,360)(244,347)(245,346)(246,348)(247,344)(248,343)(249,345)(250,350)(251,349)(252,351)(253,338)(254,337)(255,339)(256,335)(257,334)(258,336)(259,341)(260,340)(261,342)(262,329)(263,328)(264,330)(265,326)(266,325)(267,327)(268,332)(269,331)(270,333);; s1 := ( 1,190)( 2,192)( 3,191)( 4,196)( 5,198)( 6,197)( 7,193)( 8,195)( 9,194)( 10,181)( 11,183)( 12,182)( 13,187)( 14,189)( 15,188)( 16,184)( 17,186)( 18,185)( 19,217)( 20,219)( 21,218)( 22,223)( 23,225)( 24,224)( 25,220)( 26,222)( 27,221)( 28,208)( 29,210)( 30,209)( 31,214)( 32,216)( 33,215)( 34,211)( 35,213)( 36,212)( 37,199)( 38,201)( 39,200)( 40,205)( 41,207)( 42,206)( 43,202)( 44,204)( 45,203)( 46,145)( 47,147)( 48,146)( 49,151)( 50,153)( 51,152)( 52,148)( 53,150)( 54,149)( 55,136)( 56,138)( 57,137)( 58,142)( 59,144)( 60,143)( 61,139)( 62,141)( 63,140)( 64,172)( 65,174)( 66,173)( 67,178)( 68,180)( 69,179)( 70,175)( 71,177)( 72,176)( 73,163)( 74,165)( 75,164)( 76,169)( 77,171)( 78,170)( 79,166)( 80,168)( 81,167)( 82,154)( 83,156)( 84,155)( 85,160)( 86,162)( 87,161)( 88,157)( 89,159)( 90,158)( 91,236)( 92,235)( 93,237)( 94,242)( 95,241)( 96,243)( 97,239)( 98,238)( 99,240)(100,227)(101,226)(102,228)(103,233)(104,232)(105,234)(106,230)(107,229)(108,231)(109,263)(110,262)(111,264)(112,269)(113,268)(114,270)(115,266)(116,265)(117,267)(118,254)(119,253)(120,255)(121,260)(122,259)(123,261)(124,257)(125,256)(126,258)(127,245)(128,244)(129,246)(130,251)(131,250)(132,252)(133,248)(134,247)(135,249)(271,328)(272,330)(273,329)(274,325)(275,327)(276,326)(277,331)(278,333)(279,332)(280,319)(281,321)(282,320)(283,316)(284,318)(285,317)(286,322)(287,324)(288,323)(289,355)(290,357)(291,356)(292,352)(293,354)(294,353)(295,358)(296,360)(297,359)(298,346)(299,348)(300,347)(301,343)(302,345)(303,344)(304,349)(305,351)(306,350)(307,337)(308,339)(309,338)(310,334)(311,336)(312,335)(313,340)(314,342)(315,341)(361,374)(362,373)(363,375)(364,371)(365,370)(366,372)(367,377)(368,376)(369,378)(379,401)(380,400)(381,402)(382,398)(383,397)(384,399)(385,404)(386,403)(387,405)(388,392)(389,391)(390,393)(394,395);; 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)( 46, 92)( 47, 91)( 48, 93)( 49, 95)( 50, 94)( 51, 96)( 52, 98)( 53, 97)( 54, 99)( 55,101)( 56,100)( 57,102)( 58,104)( 59,103)( 60,105)( 61,107)( 62,106)( 63,108)( 64,110)( 65,109)( 66,111)( 67,113)( 68,112)( 69,114)( 70,116)( 71,115)( 72,117)( 73,119)( 74,118)( 75,120)( 76,122)( 77,121)( 78,123)( 79,125)( 80,124)( 81,126)( 82,128)( 83,127)( 84,129)( 85,131)( 86,130)( 87,132)( 88,134)( 89,133)( 90,135)(137,138)(140,141)(143,144)(146,147)(149,150)(152,153)(155,156)(158,159)(161,162)(164,165)(167,168)(170,171)(173,174)(176,177)(179,180)(181,227)(182,226)(183,228)(184,230)(185,229)(186,231)(187,233)(188,232)(189,234)(190,236)(191,235)(192,237)(193,239)(194,238)(195,240)(196,242)(197,241)(198,243)(199,245)(200,244)(201,246)(202,248)(203,247)(204,249)(205,251)(206,250)(207,252)(208,254)(209,253)(210,255)(211,257)(212,256)(213,258)(214,260)(215,259)(216,261)(217,263)(218,262)(219,264)(220,266)(221,265)(222,267)(223,269)(224,268)(225,270)(272,273)(275,276)(278,279)(281,282)(284,285)(287,288)(290,291)(293,294)(296,297)(299,300)(302,303)(305,306)(308,309)(311,312)(314,315)(316,362)(317,361)(318,363)(319,365)(320,364)(321,366)(322,368)(323,367)(324,369)(325,371)(326,370)(327,372)(328,374)(329,373)(330,375)(331,377)(332,376)(333,378)(334,380)(335,379)(336,381)(337,383)(338,382)(339,384)(340,386)(341,385)(342,387)(343,389)(344,388)(345,390)(346,392)(347,391)(348,393)(349,395)(350,394)(351,396)(352,398)(353,397)(354,399)(355,401)(356,400)(357,402)(358,404)(359,403)(360,405);; 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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(405)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 10, 37)( 11, 39)( 12, 38)( 13, 43)( 14, 45)( 15, 44)( 16, 40)( 17, 42)( 18, 41)( 19, 28)( 20, 30)( 21, 29)( 22, 34)( 23, 36)( 24, 35)( 25, 31)( 26, 33)( 27, 32)( 46, 92)( 47, 91)( 48, 93)( 49, 98)( 50, 97)( 51, 99)( 52, 95)( 53, 94)( 54, 96)( 55,128)( 56,127)( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,119)( 65,118)( 66,120)( 67,125)( 68,124)( 69,126)( 70,122)( 71,121)( 72,123)( 73,110)( 74,109)( 75,111)( 76,116)( 77,115)( 78,117)( 79,113)( 80,112)( 81,114)( 82,101)( 83,100)( 84,102)( 85,107)( 86,106)( 87,108)( 88,104)( 89,103)( 90,105)(136,274)(137,276)(138,275)(139,271)(140,273)(141,272)(142,277)(143,279)(144,278)(145,310)(146,312)(147,311)(148,307)(149,309)(150,308)(151,313)(152,315)(153,314)(154,301)(155,303)(156,302)(157,298)(158,300)(159,299)(160,304)(161,306)(162,305)(163,292)(164,294)(165,293)(166,289)(167,291)(168,290)(169,295)(170,297)(171,296)(172,283)(173,285)(174,284)(175,280)(176,282)(177,281)(178,286)(179,288)(180,287)(181,365)(182,364)(183,366)(184,362)(185,361)(186,363)(187,368)(188,367)(189,369)(190,401)(191,400)(192,402)(193,398)(194,397)(195,399)(196,404)(197,403)(198,405)(199,392)(200,391)(201,393)(202,389)(203,388)(204,390)(205,395)(206,394)(207,396)(208,383)(209,382)(210,384)(211,380)(212,379)(213,381)(214,386)(215,385)(216,387)(217,374)(218,373)(219,375)(220,371)(221,370)(222,372)(223,377)(224,376)(225,378)(226,320)(227,319)(228,321)(229,317)(230,316)(231,318)(232,323)(233,322)(234,324)(235,356)(236,355)(237,357)(238,353)(239,352)(240,354)(241,359)(242,358)(243,360)(244,347)(245,346)(246,348)(247,344)(248,343)(249,345)(250,350)(251,349)(252,351)(253,338)(254,337)(255,339)(256,335)(257,334)(258,336)(259,341)(260,340)(261,342)(262,329)(263,328)(264,330)(265,326)(266,325)(267,327)(268,332)(269,331)(270,333); s1 := Sym(405)!( 1,190)( 2,192)( 3,191)( 4,196)( 5,198)( 6,197)( 7,193)( 8,195)( 9,194)( 10,181)( 11,183)( 12,182)( 13,187)( 14,189)( 15,188)( 16,184)( 17,186)( 18,185)( 19,217)( 20,219)( 21,218)( 22,223)( 23,225)( 24,224)( 25,220)( 26,222)( 27,221)( 28,208)( 29,210)( 30,209)( 31,214)( 32,216)( 33,215)( 34,211)( 35,213)( 36,212)( 37,199)( 38,201)( 39,200)( 40,205)( 41,207)( 42,206)( 43,202)( 44,204)( 45,203)( 46,145)( 47,147)( 48,146)( 49,151)( 50,153)( 51,152)( 52,148)( 53,150)( 54,149)( 55,136)( 56,138)( 57,137)( 58,142)( 59,144)( 60,143)( 61,139)( 62,141)( 63,140)( 64,172)( 65,174)( 66,173)( 67,178)( 68,180)( 69,179)( 70,175)( 71,177)( 72,176)( 73,163)( 74,165)( 75,164)( 76,169)( 77,171)( 78,170)( 79,166)( 80,168)( 81,167)( 82,154)( 83,156)( 84,155)( 85,160)( 86,162)( 87,161)( 88,157)( 89,159)( 90,158)( 91,236)( 92,235)( 93,237)( 94,242)( 95,241)( 96,243)( 97,239)( 98,238)( 99,240)(100,227)(101,226)(102,228)(103,233)(104,232)(105,234)(106,230)(107,229)(108,231)(109,263)(110,262)(111,264)(112,269)(113,268)(114,270)(115,266)(116,265)(117,267)(118,254)(119,253)(120,255)(121,260)(122,259)(123,261)(124,257)(125,256)(126,258)(127,245)(128,244)(129,246)(130,251)(131,250)(132,252)(133,248)(134,247)(135,249)(271,328)(272,330)(273,329)(274,325)(275,327)(276,326)(277,331)(278,333)(279,332)(280,319)(281,321)(282,320)(283,316)(284,318)(285,317)(286,322)(287,324)(288,323)(289,355)(290,357)(291,356)(292,352)(293,354)(294,353)(295,358)(296,360)(297,359)(298,346)(299,348)(300,347)(301,343)(302,345)(303,344)(304,349)(305,351)(306,350)(307,337)(308,339)(309,338)(310,334)(311,336)(312,335)(313,340)(314,342)(315,341)(361,374)(362,373)(363,375)(364,371)(365,370)(366,372)(367,377)(368,376)(369,378)(379,401)(380,400)(381,402)(382,398)(383,397)(384,399)(385,404)(386,403)(387,405)(388,392)(389,391)(390,393)(394,395); s2 := Sym(405)!( 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)( 46, 92)( 47, 91)( 48, 93)( 49, 95)( 50, 94)( 51, 96)( 52, 98)( 53, 97)( 54, 99)( 55,101)( 56,100)( 57,102)( 58,104)( 59,103)( 60,105)( 61,107)( 62,106)( 63,108)( 64,110)( 65,109)( 66,111)( 67,113)( 68,112)( 69,114)( 70,116)( 71,115)( 72,117)( 73,119)( 74,118)( 75,120)( 76,122)( 77,121)( 78,123)( 79,125)( 80,124)( 81,126)( 82,128)( 83,127)( 84,129)( 85,131)( 86,130)( 87,132)( 88,134)( 89,133)( 90,135)(137,138)(140,141)(143,144)(146,147)(149,150)(152,153)(155,156)(158,159)(161,162)(164,165)(167,168)(170,171)(173,174)(176,177)(179,180)(181,227)(182,226)(183,228)(184,230)(185,229)(186,231)(187,233)(188,232)(189,234)(190,236)(191,235)(192,237)(193,239)(194,238)(195,240)(196,242)(197,241)(198,243)(199,245)(200,244)(201,246)(202,248)(203,247)(204,249)(205,251)(206,250)(207,252)(208,254)(209,253)(210,255)(211,257)(212,256)(213,258)(214,260)(215,259)(216,261)(217,263)(218,262)(219,264)(220,266)(221,265)(222,267)(223,269)(224,268)(225,270)(272,273)(275,276)(278,279)(281,282)(284,285)(287,288)(290,291)(293,294)(296,297)(299,300)(302,303)(305,306)(308,309)(311,312)(314,315)(316,362)(317,361)(318,363)(319,365)(320,364)(321,366)(322,368)(323,367)(324,369)(325,371)(326,370)(327,372)(328,374)(329,373)(330,375)(331,377)(332,376)(333,378)(334,380)(335,379)(336,381)(337,383)(338,382)(339,384)(340,386)(341,385)(342,387)(343,389)(344,388)(345,390)(346,392)(347,391)(348,393)(349,395)(350,394)(351,396)(352,398)(353,397)(354,399)(355,401)(356,400)(357,402)(358,404)(359,403)(360,405); poly := sub<Sym(405)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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.