Polytope of Type {10,76}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,76}*1520
Also Known As : {10,76|2}. if this polytope has another name.
Group : SmallGroup(1520,121)
Rank : 3
Schlafli Type : {10,76}
Number of vertices, edges, etc : 10, 380, 76
Order of s0s1s2 : 380
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {10,38}*760
5-fold quotients : {2,76}*304
10-fold quotients : {2,38}*152
19-fold quotients : {10,4}*80
20-fold quotients : {2,19}*76
38-fold quotients : {10,2}*40
76-fold quotients : {5,2}*20
95-fold quotients : {2,4}*16
190-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 20, 77)( 21, 78)( 22, 79)( 23, 80)( 24, 81)( 25, 82)( 26, 83)( 27, 84)
( 28, 85)( 29, 86)( 30, 87)( 31, 88)( 32, 89)( 33, 90)( 34, 91)( 35, 92)
( 36, 93)( 37, 94)( 38, 95)( 39, 58)( 40, 59)( 41, 60)( 42, 61)( 43, 62)
( 44, 63)( 45, 64)( 46, 65)( 47, 66)( 48, 67)( 49, 68)( 50, 69)( 51, 70)
( 52, 71)( 53, 72)( 54, 73)( 55, 74)( 56, 75)( 57, 76)(115,172)(116,173)
(117,174)(118,175)(119,176)(120,177)(121,178)(122,179)(123,180)(124,181)
(125,182)(126,183)(127,184)(128,185)(129,186)(130,187)(131,188)(132,189)
(133,190)(134,153)(135,154)(136,155)(137,156)(138,157)(139,158)(140,159)
(141,160)(142,161)(143,162)(144,163)(145,164)(146,165)(147,166)(148,167)
(149,168)(150,169)(151,170)(152,171)(210,267)(211,268)(212,269)(213,270)
(214,271)(215,272)(216,273)(217,274)(218,275)(219,276)(220,277)(221,278)
(222,279)(223,280)(224,281)(225,282)(226,283)(227,284)(228,285)(229,248)
(230,249)(231,250)(232,251)(233,252)(234,253)(235,254)(236,255)(237,256)
(238,257)(239,258)(240,259)(241,260)(242,261)(243,262)(244,263)(245,264)
(246,265)(247,266)(305,362)(306,363)(307,364)(308,365)(309,366)(310,367)
(311,368)(312,369)(313,370)(314,371)(315,372)(316,373)(317,374)(318,375)
(319,376)(320,377)(321,378)(322,379)(323,380)(324,343)(325,344)(326,345)
(327,346)(328,347)(329,348)(330,349)(331,350)(332,351)(333,352)(334,353)
(335,354)(336,355)(337,356)(338,357)(339,358)(340,359)(341,360)(342,361);;
s1 := ( 1, 20)( 2, 38)( 3, 37)( 4, 36)( 5, 35)( 6, 34)( 7, 33)( 8, 32)
( 9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)( 16, 24)
( 17, 23)( 18, 22)( 19, 21)( 39, 77)( 40, 95)( 41, 94)( 42, 93)( 43, 92)
( 44, 91)( 45, 90)( 46, 89)( 47, 88)( 48, 87)( 49, 86)( 50, 85)( 51, 84)
( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 79)( 57, 78)( 59, 76)( 60, 75)
( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)( 96,115)
( 97,133)( 98,132)( 99,131)(100,130)(101,129)(102,128)(103,127)(104,126)
(105,125)(106,124)(107,123)(108,122)(109,121)(110,120)(111,119)(112,118)
(113,117)(114,116)(134,172)(135,190)(136,189)(137,188)(138,187)(139,186)
(140,185)(141,184)(142,183)(143,182)(144,181)(145,180)(146,179)(147,178)
(148,177)(149,176)(150,175)(151,174)(152,173)(154,171)(155,170)(156,169)
(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)(191,305)(192,323)
(193,322)(194,321)(195,320)(196,319)(197,318)(198,317)(199,316)(200,315)
(201,314)(202,313)(203,312)(204,311)(205,310)(206,309)(207,308)(208,307)
(209,306)(210,286)(211,304)(212,303)(213,302)(214,301)(215,300)(216,299)
(217,298)(218,297)(219,296)(220,295)(221,294)(222,293)(223,292)(224,291)
(225,290)(226,289)(227,288)(228,287)(229,362)(230,380)(231,379)(232,378)
(233,377)(234,376)(235,375)(236,374)(237,373)(238,372)(239,371)(240,370)
(241,369)(242,368)(243,367)(244,366)(245,365)(246,364)(247,363)(248,343)
(249,361)(250,360)(251,359)(252,358)(253,357)(254,356)(255,355)(256,354)
(257,353)(258,352)(259,351)(260,350)(261,349)(262,348)(263,347)(264,346)
(265,345)(266,344)(267,324)(268,342)(269,341)(270,340)(271,339)(272,338)
(273,337)(274,336)(275,335)(276,334)(277,333)(278,332)(279,331)(280,330)
(281,329)(282,328)(283,327)(284,326)(285,325);;
s2 := ( 1,192)( 2,191)( 3,209)( 4,208)( 5,207)( 6,206)( 7,205)( 8,204)
( 9,203)( 10,202)( 11,201)( 12,200)( 13,199)( 14,198)( 15,197)( 16,196)
( 17,195)( 18,194)( 19,193)( 20,211)( 21,210)( 22,228)( 23,227)( 24,226)
( 25,225)( 26,224)( 27,223)( 28,222)( 29,221)( 30,220)( 31,219)( 32,218)
( 33,217)( 34,216)( 35,215)( 36,214)( 37,213)( 38,212)( 39,230)( 40,229)
( 41,247)( 42,246)( 43,245)( 44,244)( 45,243)( 46,242)( 47,241)( 48,240)
( 49,239)( 50,238)( 51,237)( 52,236)( 53,235)( 54,234)( 55,233)( 56,232)
( 57,231)( 58,249)( 59,248)( 60,266)( 61,265)( 62,264)( 63,263)( 64,262)
( 65,261)( 66,260)( 67,259)( 68,258)( 69,257)( 70,256)( 71,255)( 72,254)
( 73,253)( 74,252)( 75,251)( 76,250)( 77,268)( 78,267)( 79,285)( 80,284)
( 81,283)( 82,282)( 83,281)( 84,280)( 85,279)( 86,278)( 87,277)( 88,276)
( 89,275)( 90,274)( 91,273)( 92,272)( 93,271)( 94,270)( 95,269)( 96,287)
( 97,286)( 98,304)( 99,303)(100,302)(101,301)(102,300)(103,299)(104,298)
(105,297)(106,296)(107,295)(108,294)(109,293)(110,292)(111,291)(112,290)
(113,289)(114,288)(115,306)(116,305)(117,323)(118,322)(119,321)(120,320)
(121,319)(122,318)(123,317)(124,316)(125,315)(126,314)(127,313)(128,312)
(129,311)(130,310)(131,309)(132,308)(133,307)(134,325)(135,324)(136,342)
(137,341)(138,340)(139,339)(140,338)(141,337)(142,336)(143,335)(144,334)
(145,333)(146,332)(147,331)(148,330)(149,329)(150,328)(151,327)(152,326)
(153,344)(154,343)(155,361)(156,360)(157,359)(158,358)(159,357)(160,356)
(161,355)(162,354)(163,353)(164,352)(165,351)(166,350)(167,349)(168,348)
(169,347)(170,346)(171,345)(172,363)(173,362)(174,380)(175,379)(176,378)
(177,377)(178,376)(179,375)(180,374)(181,373)(182,372)(183,371)(184,370)
(185,369)(186,368)(187,367)(188,366)(189,365)(190,364);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(380)!( 20, 77)( 21, 78)( 22, 79)( 23, 80)( 24, 81)( 25, 82)( 26, 83)
( 27, 84)( 28, 85)( 29, 86)( 30, 87)( 31, 88)( 32, 89)( 33, 90)( 34, 91)
( 35, 92)( 36, 93)( 37, 94)( 38, 95)( 39, 58)( 40, 59)( 41, 60)( 42, 61)
( 43, 62)( 44, 63)( 45, 64)( 46, 65)( 47, 66)( 48, 67)( 49, 68)( 50, 69)
( 51, 70)( 52, 71)( 53, 72)( 54, 73)( 55, 74)( 56, 75)( 57, 76)(115,172)
(116,173)(117,174)(118,175)(119,176)(120,177)(121,178)(122,179)(123,180)
(124,181)(125,182)(126,183)(127,184)(128,185)(129,186)(130,187)(131,188)
(132,189)(133,190)(134,153)(135,154)(136,155)(137,156)(138,157)(139,158)
(140,159)(141,160)(142,161)(143,162)(144,163)(145,164)(146,165)(147,166)
(148,167)(149,168)(150,169)(151,170)(152,171)(210,267)(211,268)(212,269)
(213,270)(214,271)(215,272)(216,273)(217,274)(218,275)(219,276)(220,277)
(221,278)(222,279)(223,280)(224,281)(225,282)(226,283)(227,284)(228,285)
(229,248)(230,249)(231,250)(232,251)(233,252)(234,253)(235,254)(236,255)
(237,256)(238,257)(239,258)(240,259)(241,260)(242,261)(243,262)(244,263)
(245,264)(246,265)(247,266)(305,362)(306,363)(307,364)(308,365)(309,366)
(310,367)(311,368)(312,369)(313,370)(314,371)(315,372)(316,373)(317,374)
(318,375)(319,376)(320,377)(321,378)(322,379)(323,380)(324,343)(325,344)
(326,345)(327,346)(328,347)(329,348)(330,349)(331,350)(332,351)(333,352)
(334,353)(335,354)(336,355)(337,356)(338,357)(339,358)(340,359)(341,360)
(342,361);
s1 := Sym(380)!( 1, 20)( 2, 38)( 3, 37)( 4, 36)( 5, 35)( 6, 34)( 7, 33)
( 8, 32)( 9, 31)( 10, 30)( 11, 29)( 12, 28)( 13, 27)( 14, 26)( 15, 25)
( 16, 24)( 17, 23)( 18, 22)( 19, 21)( 39, 77)( 40, 95)( 41, 94)( 42, 93)
( 43, 92)( 44, 91)( 45, 90)( 46, 89)( 47, 88)( 48, 87)( 49, 86)( 50, 85)
( 51, 84)( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 79)( 57, 78)( 59, 76)
( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 67, 68)
( 96,115)( 97,133)( 98,132)( 99,131)(100,130)(101,129)(102,128)(103,127)
(104,126)(105,125)(106,124)(107,123)(108,122)(109,121)(110,120)(111,119)
(112,118)(113,117)(114,116)(134,172)(135,190)(136,189)(137,188)(138,187)
(139,186)(140,185)(141,184)(142,183)(143,182)(144,181)(145,180)(146,179)
(147,178)(148,177)(149,176)(150,175)(151,174)(152,173)(154,171)(155,170)
(156,169)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)(191,305)
(192,323)(193,322)(194,321)(195,320)(196,319)(197,318)(198,317)(199,316)
(200,315)(201,314)(202,313)(203,312)(204,311)(205,310)(206,309)(207,308)
(208,307)(209,306)(210,286)(211,304)(212,303)(213,302)(214,301)(215,300)
(216,299)(217,298)(218,297)(219,296)(220,295)(221,294)(222,293)(223,292)
(224,291)(225,290)(226,289)(227,288)(228,287)(229,362)(230,380)(231,379)
(232,378)(233,377)(234,376)(235,375)(236,374)(237,373)(238,372)(239,371)
(240,370)(241,369)(242,368)(243,367)(244,366)(245,365)(246,364)(247,363)
(248,343)(249,361)(250,360)(251,359)(252,358)(253,357)(254,356)(255,355)
(256,354)(257,353)(258,352)(259,351)(260,350)(261,349)(262,348)(263,347)
(264,346)(265,345)(266,344)(267,324)(268,342)(269,341)(270,340)(271,339)
(272,338)(273,337)(274,336)(275,335)(276,334)(277,333)(278,332)(279,331)
(280,330)(281,329)(282,328)(283,327)(284,326)(285,325);
s2 := Sym(380)!( 1,192)( 2,191)( 3,209)( 4,208)( 5,207)( 6,206)( 7,205)
( 8,204)( 9,203)( 10,202)( 11,201)( 12,200)( 13,199)( 14,198)( 15,197)
( 16,196)( 17,195)( 18,194)( 19,193)( 20,211)( 21,210)( 22,228)( 23,227)
( 24,226)( 25,225)( 26,224)( 27,223)( 28,222)( 29,221)( 30,220)( 31,219)
( 32,218)( 33,217)( 34,216)( 35,215)( 36,214)( 37,213)( 38,212)( 39,230)
( 40,229)( 41,247)( 42,246)( 43,245)( 44,244)( 45,243)( 46,242)( 47,241)
( 48,240)( 49,239)( 50,238)( 51,237)( 52,236)( 53,235)( 54,234)( 55,233)
( 56,232)( 57,231)( 58,249)( 59,248)( 60,266)( 61,265)( 62,264)( 63,263)
( 64,262)( 65,261)( 66,260)( 67,259)( 68,258)( 69,257)( 70,256)( 71,255)
( 72,254)( 73,253)( 74,252)( 75,251)( 76,250)( 77,268)( 78,267)( 79,285)
( 80,284)( 81,283)( 82,282)( 83,281)( 84,280)( 85,279)( 86,278)( 87,277)
( 88,276)( 89,275)( 90,274)( 91,273)( 92,272)( 93,271)( 94,270)( 95,269)
( 96,287)( 97,286)( 98,304)( 99,303)(100,302)(101,301)(102,300)(103,299)
(104,298)(105,297)(106,296)(107,295)(108,294)(109,293)(110,292)(111,291)
(112,290)(113,289)(114,288)(115,306)(116,305)(117,323)(118,322)(119,321)
(120,320)(121,319)(122,318)(123,317)(124,316)(125,315)(126,314)(127,313)
(128,312)(129,311)(130,310)(131,309)(132,308)(133,307)(134,325)(135,324)
(136,342)(137,341)(138,340)(139,339)(140,338)(141,337)(142,336)(143,335)
(144,334)(145,333)(146,332)(147,331)(148,330)(149,329)(150,328)(151,327)
(152,326)(153,344)(154,343)(155,361)(156,360)(157,359)(158,358)(159,357)
(160,356)(161,355)(162,354)(163,353)(164,352)(165,351)(166,350)(167,349)
(168,348)(169,347)(170,346)(171,345)(172,363)(173,362)(174,380)(175,379)
(176,378)(177,377)(178,376)(179,375)(180,374)(181,373)(182,372)(183,371)
(184,370)(185,369)(186,368)(187,367)(188,366)(189,365)(190,364);
poly := sub<Sym(380)|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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope