Polytope of Type {10,75}

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

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