Polytope of Type {10,74}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,74}*1480
Also Known As : {10,74|2}. if this polytope has another name.
Group : SmallGroup(1480,45)
Rank : 3
Schlafli Type : {10,74}
Number of vertices, edges, etc : 10, 370, 74
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 : {2,74}*296
10-fold quotients : {2,37}*148
37-fold quotients : {10,2}*40
74-fold quotients : {5,2}*20
185-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 38,149)( 39,150)( 40,151)( 41,152)( 42,153)( 43,154)( 44,155)( 45,156)
( 46,157)( 47,158)( 48,159)( 49,160)( 50,161)( 51,162)( 52,163)( 53,164)
( 54,165)( 55,166)( 56,167)( 57,168)( 58,169)( 59,170)( 60,171)( 61,172)
( 62,173)( 63,174)( 64,175)( 65,176)( 66,177)( 67,178)( 68,179)( 69,180)
( 70,181)( 71,182)( 72,183)( 73,184)( 74,185)( 75,112)( 76,113)( 77,114)
( 78,115)( 79,116)( 80,117)( 81,118)( 82,119)( 83,120)( 84,121)( 85,122)
( 86,123)( 87,124)( 88,125)( 89,126)( 90,127)( 91,128)( 92,129)( 93,130)
( 94,131)( 95,132)( 96,133)( 97,134)( 98,135)( 99,136)(100,137)(101,138)
(102,139)(103,140)(104,141)(105,142)(106,143)(107,144)(108,145)(109,146)
(110,147)(111,148)(223,334)(224,335)(225,336)(226,337)(227,338)(228,339)
(229,340)(230,341)(231,342)(232,343)(233,344)(234,345)(235,346)(236,347)
(237,348)(238,349)(239,350)(240,351)(241,352)(242,353)(243,354)(244,355)
(245,356)(246,357)(247,358)(248,359)(249,360)(250,361)(251,362)(252,363)
(253,364)(254,365)(255,366)(256,367)(257,368)(258,369)(259,370)(260,297)
(261,298)(262,299)(263,300)(264,301)(265,302)(266,303)(267,304)(268,305)
(269,306)(270,307)(271,308)(272,309)(273,310)(274,311)(275,312)(276,313)
(277,314)(278,315)(279,316)(280,317)(281,318)(282,319)(283,320)(284,321)
(285,322)(286,323)(287,324)(288,325)(289,326)(290,327)(291,328)(292,329)
(293,330)(294,331)(295,332)(296,333);;
s1 := ( 1, 38)( 2, 74)( 3, 73)( 4, 72)( 5, 71)( 6, 70)( 7, 69)( 8, 68)
( 9, 67)( 10, 66)( 11, 65)( 12, 64)( 13, 63)( 14, 62)( 15, 61)( 16, 60)
( 17, 59)( 18, 58)( 19, 57)( 20, 56)( 21, 55)( 22, 54)( 23, 53)( 24, 52)
( 25, 51)( 26, 50)( 27, 49)( 28, 48)( 29, 47)( 30, 46)( 31, 45)( 32, 44)
( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 75,149)( 76,185)( 77,184)
( 78,183)( 79,182)( 80,181)( 81,180)( 82,179)( 83,178)( 84,177)( 85,176)
( 86,175)( 87,174)( 88,173)( 89,172)( 90,171)( 91,170)( 92,169)( 93,168)
( 94,167)( 95,166)( 96,165)( 97,164)( 98,163)( 99,162)(100,161)(101,160)
(102,159)(103,158)(104,157)(105,156)(106,155)(107,154)(108,153)(109,152)
(110,151)(111,150)(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)(186,223)(187,259)(188,258)(189,257)
(190,256)(191,255)(192,254)(193,253)(194,252)(195,251)(196,250)(197,249)
(198,248)(199,247)(200,246)(201,245)(202,244)(203,243)(204,242)(205,241)
(206,240)(207,239)(208,238)(209,237)(210,236)(211,235)(212,234)(213,233)
(214,232)(215,231)(216,230)(217,229)(218,228)(219,227)(220,226)(221,225)
(222,224)(260,334)(261,370)(262,369)(263,368)(264,367)(265,366)(266,365)
(267,364)(268,363)(269,362)(270,361)(271,360)(272,359)(273,358)(274,357)
(275,356)(276,355)(277,354)(278,353)(279,352)(280,351)(281,350)(282,349)
(283,348)(284,347)(285,346)(286,345)(287,344)(288,343)(289,342)(290,341)
(291,340)(292,339)(293,338)(294,337)(295,336)(296,335)(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);;
s2 := ( 1,187)( 2,186)( 3,222)( 4,221)( 5,220)( 6,219)( 7,218)( 8,217)
( 9,216)( 10,215)( 11,214)( 12,213)( 13,212)( 14,211)( 15,210)( 16,209)
( 17,208)( 18,207)( 19,206)( 20,205)( 21,204)( 22,203)( 23,202)( 24,201)
( 25,200)( 26,199)( 27,198)( 28,197)( 29,196)( 30,195)( 31,194)( 32,193)
( 33,192)( 34,191)( 35,190)( 36,189)( 37,188)( 38,224)( 39,223)( 40,259)
( 41,258)( 42,257)( 43,256)( 44,255)( 45,254)( 46,253)( 47,252)( 48,251)
( 49,250)( 50,249)( 51,248)( 52,247)( 53,246)( 54,245)( 55,244)( 56,243)
( 57,242)( 58,241)( 59,240)( 60,239)( 61,238)( 62,237)( 63,236)( 64,235)
( 65,234)( 66,233)( 67,232)( 68,231)( 69,230)( 70,229)( 71,228)( 72,227)
( 73,226)( 74,225)( 75,261)( 76,260)( 77,296)( 78,295)( 79,294)( 80,293)
( 81,292)( 82,291)( 83,290)( 84,289)( 85,288)( 86,287)( 87,286)( 88,285)
( 89,284)( 90,283)( 91,282)( 92,281)( 93,280)( 94,279)( 95,278)( 96,277)
( 97,276)( 98,275)( 99,274)(100,273)(101,272)(102,271)(103,270)(104,269)
(105,268)(106,267)(107,266)(108,265)(109,264)(110,263)(111,262)(112,298)
(113,297)(114,333)(115,332)(116,331)(117,330)(118,329)(119,328)(120,327)
(121,326)(122,325)(123,324)(124,323)(125,322)(126,321)(127,320)(128,319)
(129,318)(130,317)(131,316)(132,315)(133,314)(134,313)(135,312)(136,311)
(137,310)(138,309)(139,308)(140,307)(141,306)(142,305)(143,304)(144,303)
(145,302)(146,301)(147,300)(148,299)(149,335)(150,334)(151,370)(152,369)
(153,368)(154,367)(155,366)(156,365)(157,364)(158,363)(159,362)(160,361)
(161,360)(162,359)(163,358)(164,357)(165,356)(166,355)(167,354)(168,353)
(169,352)(170,351)(171,350)(172,349)(173,348)(174,347)(175,346)(176,345)
(177,344)(178,343)(179,342)(180,341)(181,340)(182,339)(183,338)(184,337)
(185,336);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(370)!( 38,149)( 39,150)( 40,151)( 41,152)( 42,153)( 43,154)( 44,155)
( 45,156)( 46,157)( 47,158)( 48,159)( 49,160)( 50,161)( 51,162)( 52,163)
( 53,164)( 54,165)( 55,166)( 56,167)( 57,168)( 58,169)( 59,170)( 60,171)
( 61,172)( 62,173)( 63,174)( 64,175)( 65,176)( 66,177)( 67,178)( 68,179)
( 69,180)( 70,181)( 71,182)( 72,183)( 73,184)( 74,185)( 75,112)( 76,113)
( 77,114)( 78,115)( 79,116)( 80,117)( 81,118)( 82,119)( 83,120)( 84,121)
( 85,122)( 86,123)( 87,124)( 88,125)( 89,126)( 90,127)( 91,128)( 92,129)
( 93,130)( 94,131)( 95,132)( 96,133)( 97,134)( 98,135)( 99,136)(100,137)
(101,138)(102,139)(103,140)(104,141)(105,142)(106,143)(107,144)(108,145)
(109,146)(110,147)(111,148)(223,334)(224,335)(225,336)(226,337)(227,338)
(228,339)(229,340)(230,341)(231,342)(232,343)(233,344)(234,345)(235,346)
(236,347)(237,348)(238,349)(239,350)(240,351)(241,352)(242,353)(243,354)
(244,355)(245,356)(246,357)(247,358)(248,359)(249,360)(250,361)(251,362)
(252,363)(253,364)(254,365)(255,366)(256,367)(257,368)(258,369)(259,370)
(260,297)(261,298)(262,299)(263,300)(264,301)(265,302)(266,303)(267,304)
(268,305)(269,306)(270,307)(271,308)(272,309)(273,310)(274,311)(275,312)
(276,313)(277,314)(278,315)(279,316)(280,317)(281,318)(282,319)(283,320)
(284,321)(285,322)(286,323)(287,324)(288,325)(289,326)(290,327)(291,328)
(292,329)(293,330)(294,331)(295,332)(296,333);
s1 := Sym(370)!( 1, 38)( 2, 74)( 3, 73)( 4, 72)( 5, 71)( 6, 70)( 7, 69)
( 8, 68)( 9, 67)( 10, 66)( 11, 65)( 12, 64)( 13, 63)( 14, 62)( 15, 61)
( 16, 60)( 17, 59)( 18, 58)( 19, 57)( 20, 56)( 21, 55)( 22, 54)( 23, 53)
( 24, 52)( 25, 51)( 26, 50)( 27, 49)( 28, 48)( 29, 47)( 30, 46)( 31, 45)
( 32, 44)( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 37, 39)( 75,149)( 76,185)
( 77,184)( 78,183)( 79,182)( 80,181)( 81,180)( 82,179)( 83,178)( 84,177)
( 85,176)( 86,175)( 87,174)( 88,173)( 89,172)( 90,171)( 91,170)( 92,169)
( 93,168)( 94,167)( 95,166)( 96,165)( 97,164)( 98,163)( 99,162)(100,161)
(101,160)(102,159)(103,158)(104,157)(105,156)(106,155)(107,154)(108,153)
(109,152)(110,151)(111,150)(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)(186,223)(187,259)(188,258)
(189,257)(190,256)(191,255)(192,254)(193,253)(194,252)(195,251)(196,250)
(197,249)(198,248)(199,247)(200,246)(201,245)(202,244)(203,243)(204,242)
(205,241)(206,240)(207,239)(208,238)(209,237)(210,236)(211,235)(212,234)
(213,233)(214,232)(215,231)(216,230)(217,229)(218,228)(219,227)(220,226)
(221,225)(222,224)(260,334)(261,370)(262,369)(263,368)(264,367)(265,366)
(266,365)(267,364)(268,363)(269,362)(270,361)(271,360)(272,359)(273,358)
(274,357)(275,356)(276,355)(277,354)(278,353)(279,352)(280,351)(281,350)
(282,349)(283,348)(284,347)(285,346)(286,345)(287,344)(288,343)(289,342)
(290,341)(291,340)(292,339)(293,338)(294,337)(295,336)(296,335)(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);
s2 := Sym(370)!( 1,187)( 2,186)( 3,222)( 4,221)( 5,220)( 6,219)( 7,218)
( 8,217)( 9,216)( 10,215)( 11,214)( 12,213)( 13,212)( 14,211)( 15,210)
( 16,209)( 17,208)( 18,207)( 19,206)( 20,205)( 21,204)( 22,203)( 23,202)
( 24,201)( 25,200)( 26,199)( 27,198)( 28,197)( 29,196)( 30,195)( 31,194)
( 32,193)( 33,192)( 34,191)( 35,190)( 36,189)( 37,188)( 38,224)( 39,223)
( 40,259)( 41,258)( 42,257)( 43,256)( 44,255)( 45,254)( 46,253)( 47,252)
( 48,251)( 49,250)( 50,249)( 51,248)( 52,247)( 53,246)( 54,245)( 55,244)
( 56,243)( 57,242)( 58,241)( 59,240)( 60,239)( 61,238)( 62,237)( 63,236)
( 64,235)( 65,234)( 66,233)( 67,232)( 68,231)( 69,230)( 70,229)( 71,228)
( 72,227)( 73,226)( 74,225)( 75,261)( 76,260)( 77,296)( 78,295)( 79,294)
( 80,293)( 81,292)( 82,291)( 83,290)( 84,289)( 85,288)( 86,287)( 87,286)
( 88,285)( 89,284)( 90,283)( 91,282)( 92,281)( 93,280)( 94,279)( 95,278)
( 96,277)( 97,276)( 98,275)( 99,274)(100,273)(101,272)(102,271)(103,270)
(104,269)(105,268)(106,267)(107,266)(108,265)(109,264)(110,263)(111,262)
(112,298)(113,297)(114,333)(115,332)(116,331)(117,330)(118,329)(119,328)
(120,327)(121,326)(122,325)(123,324)(124,323)(125,322)(126,321)(127,320)
(128,319)(129,318)(130,317)(131,316)(132,315)(133,314)(134,313)(135,312)
(136,311)(137,310)(138,309)(139,308)(140,307)(141,306)(142,305)(143,304)
(144,303)(145,302)(146,301)(147,300)(148,299)(149,335)(150,334)(151,370)
(152,369)(153,368)(154,367)(155,366)(156,365)(157,364)(158,363)(159,362)
(160,361)(161,360)(162,359)(163,358)(164,357)(165,356)(166,355)(167,354)
(168,353)(169,352)(170,351)(171,350)(172,349)(173,348)(174,347)(175,346)
(176,345)(177,344)(178,343)(179,342)(180,341)(181,340)(182,339)(183,338)
(184,337)(185,336);
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,
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 >;
References : None.
to this polytope