Polytope of Type {76,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {76,10}*1520
Also Known As : {76,10|2}. if this polytope has another name.
Group : SmallGroup(1520,121)
Rank : 3
Schlafli Type : {76,10}
Number of vertices, edges, etc : 76, 380, 10
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 : {38,10}*760
   5-fold quotients : {76,2}*304
   10-fold quotients : {38,2}*152
   19-fold quotients : {4,10}*80
   20-fold quotients : {19,2}*76
   38-fold quotients : {2,10}*40
   76-fold quotients : {2,5}*20
   95-fold quotients : {4,2}*16
   190-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope