Polytope of Type {75,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {75,10}*1500
if this polytope has a name.
Group : SmallGroup(1500,70)
Rank : 3
Schlafli Type : {75,10}
Number of vertices, edges, etc : 75, 375, 10
Order of s₀s₁s₂ : 150
Order of s₀s₁s₂s₁ : 10
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) :
   3-fold quotients : {25,10}*500
   5-fold quotients : {75,2}*300, {15,10}*300
   15-fold quotients : {25,2}*100, {5,10}*100
   25-fold quotients : {15,2}*60
   75-fold quotients : {5,2}*20
   125-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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