Polytope of Type {74,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {74,10}*1480
Also Known As : {74,10|2}. if this polytope has another name.
Group : SmallGroup(1480,45)
Rank : 3
Schlafli Type : {74,10}
Number of vertices, edges, etc : 74, 370, 10
Order of s₀s₁s₂ : 370
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) :
   5-fold quotients : {74,2}*296
   10-fold quotients : {37,2}*148
   37-fold quotients : {2,10}*40
   74-fold quotients : {2,5}*20
   185-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope