Polytope of Type {15,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,10}*1500e
if this polytope has a name.
Group : SmallGroup(1500,72)
Rank : 3
Schlafli Type : {15,10}
Number of vertices, edges, etc : 75, 375, 50
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {5,10}*500
   5-fold quotients : {15,10}*300
   15-fold quotients : {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 := (  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)
( 14, 19)( 15, 20)( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)( 31,121)
( 32,122)( 33,123)( 34,124)( 35,125)( 36,116)( 37,117)( 38,118)( 39,119)
( 40,120)( 41,111)( 42,112)( 43,113)( 44,114)( 45,115)( 46,106)( 47,107)
( 48,108)( 49,109)( 50,110)( 51, 76)( 52, 77)( 53, 78)( 54, 79)( 55, 80)
( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)( 62, 92)( 63, 93)
( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)( 71, 81)
( 72, 82)( 73, 83)( 74, 84)( 75, 85)(126,251)(127,252)(128,253)(129,254)
(130,255)(131,271)(132,272)(133,273)(134,274)(135,275)(136,266)(137,267)
(138,268)(139,269)(140,270)(141,261)(142,262)(143,263)(144,264)(145,265)
(146,256)(147,257)(148,258)(149,259)(150,260)(151,351)(152,352)(153,353)
(154,354)(155,355)(156,371)(157,372)(158,373)(159,374)(160,375)(161,366)
(162,367)(163,368)(164,369)(165,370)(166,361)(167,362)(168,363)(169,364)
(170,365)(171,356)(172,357)(173,358)(174,359)(175,360)(176,326)(177,327)
(178,328)(179,329)(180,330)(181,346)(182,347)(183,348)(184,349)(185,350)
(186,341)(187,342)(188,343)(189,344)(190,345)(191,336)(192,337)(193,338)
(194,339)(195,340)(196,331)(197,332)(198,333)(199,334)(200,335)(201,301)
(202,302)(203,303)(204,304)(205,305)(206,321)(207,322)(208,323)(209,324)
(210,325)(211,316)(212,317)(213,318)(214,319)(215,320)(216,311)(217,312)
(218,313)(219,314)(220,315)(221,306)(222,307)(223,308)(224,309)(225,310)
(226,276)(227,277)(228,278)(229,279)(230,280)(231,296)(232,297)(233,298)
(234,299)(235,300)(236,291)(237,292)(238,293)(239,294)(240,295)(241,286)
(242,287)(243,288)(244,289)(245,290)(246,281)(247,282)(248,283)(249,284)
(250,285);;
s1 := (  1,182)(  2,183)(  3,184)(  4,185)(  5,181)(  6,180)(  7,176)(  8,177)
(  9,178)( 10,179)( 11,198)( 12,199)( 13,200)( 14,196)( 15,197)( 16,191)
( 17,192)( 18,193)( 19,194)( 20,195)( 21,189)( 22,190)( 23,186)( 24,187)
( 25,188)( 26,157)( 27,158)( 28,159)( 29,160)( 30,156)( 31,155)( 32,151)
( 33,152)( 34,153)( 35,154)( 36,173)( 37,174)( 38,175)( 39,171)( 40,172)
( 41,166)( 42,167)( 43,168)( 44,169)( 45,170)( 46,164)( 47,165)( 48,161)
( 49,162)( 50,163)( 51,132)( 52,133)( 53,134)( 54,135)( 55,131)( 56,130)
( 57,126)( 58,127)( 59,128)( 60,129)( 61,148)( 62,149)( 63,150)( 64,146)
( 65,147)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,139)( 72,140)
( 73,136)( 74,137)( 75,138)( 76,232)( 77,233)( 78,234)( 79,235)( 80,231)
( 81,230)( 82,226)( 83,227)( 84,228)( 85,229)( 86,248)( 87,249)( 88,250)
( 89,246)( 90,247)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)( 96,239)
( 97,240)( 98,236)( 99,237)(100,238)(101,207)(102,208)(103,209)(104,210)
(105,206)(106,205)(107,201)(108,202)(109,203)(110,204)(111,223)(112,224)
(113,225)(114,221)(115,222)(116,216)(117,217)(118,218)(119,219)(120,220)
(121,214)(122,215)(123,211)(124,212)(125,213)(251,307)(252,308)(253,309)
(254,310)(255,306)(256,305)(257,301)(258,302)(259,303)(260,304)(261,323)
(262,324)(263,325)(264,321)(265,322)(266,316)(267,317)(268,318)(269,319)
(270,320)(271,314)(272,315)(273,311)(274,312)(275,313)(276,282)(277,283)
(278,284)(279,285)(280,281)(286,298)(287,299)(288,300)(289,296)(290,297)
(326,357)(327,358)(328,359)(329,360)(330,356)(331,355)(332,351)(333,352)
(334,353)(335,354)(336,373)(337,374)(338,375)(339,371)(340,372)(341,366)
(342,367)(343,368)(344,369)(345,370)(346,364)(347,365)(348,361)(349,362)
(350,363);;
s2 := (  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)
( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)
( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)
( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)
( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)
( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)
(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,116)
(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)(132,150)
(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)(140,142)
(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)(161,166)
(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)(182,200)
(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)(190,192)
(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)(211,216)
(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)(232,250)
(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)(240,242)
(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)(261,266)
(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)(282,300)
(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)(290,292)
(302,305)(303,304)(306,321)(307,325)(308,324)(309,323)(310,322)(311,316)
(312,320)(313,319)(314,318)(315,317)(327,330)(328,329)(331,346)(332,350)
(333,349)(334,348)(335,347)(336,341)(337,345)(338,344)(339,343)(340,342)
(352,355)(353,354)(356,371)(357,375)(358,374)(359,373)(360,372)(361,366)
(362,370)(363,369)(364,368)(365,367);;
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*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*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 ];;
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)( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)
( 31,121)( 32,122)( 33,123)( 34,124)( 35,125)( 36,116)( 37,117)( 38,118)
( 39,119)( 40,120)( 41,111)( 42,112)( 43,113)( 44,114)( 45,115)( 46,106)
( 47,107)( 48,108)( 49,109)( 50,110)( 51, 76)( 52, 77)( 53, 78)( 54, 79)
( 55, 80)( 56, 96)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61, 91)( 62, 92)
( 63, 93)( 64, 94)( 65, 95)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)
( 71, 81)( 72, 82)( 73, 83)( 74, 84)( 75, 85)(126,251)(127,252)(128,253)
(129,254)(130,255)(131,271)(132,272)(133,273)(134,274)(135,275)(136,266)
(137,267)(138,268)(139,269)(140,270)(141,261)(142,262)(143,263)(144,264)
(145,265)(146,256)(147,257)(148,258)(149,259)(150,260)(151,351)(152,352)
(153,353)(154,354)(155,355)(156,371)(157,372)(158,373)(159,374)(160,375)
(161,366)(162,367)(163,368)(164,369)(165,370)(166,361)(167,362)(168,363)
(169,364)(170,365)(171,356)(172,357)(173,358)(174,359)(175,360)(176,326)
(177,327)(178,328)(179,329)(180,330)(181,346)(182,347)(183,348)(184,349)
(185,350)(186,341)(187,342)(188,343)(189,344)(190,345)(191,336)(192,337)
(193,338)(194,339)(195,340)(196,331)(197,332)(198,333)(199,334)(200,335)
(201,301)(202,302)(203,303)(204,304)(205,305)(206,321)(207,322)(208,323)
(209,324)(210,325)(211,316)(212,317)(213,318)(214,319)(215,320)(216,311)
(217,312)(218,313)(219,314)(220,315)(221,306)(222,307)(223,308)(224,309)
(225,310)(226,276)(227,277)(228,278)(229,279)(230,280)(231,296)(232,297)
(233,298)(234,299)(235,300)(236,291)(237,292)(238,293)(239,294)(240,295)
(241,286)(242,287)(243,288)(244,289)(245,290)(246,281)(247,282)(248,283)
(249,284)(250,285);
s1 := Sym(375)!(  1,182)(  2,183)(  3,184)(  4,185)(  5,181)(  6,180)(  7,176)
(  8,177)(  9,178)( 10,179)( 11,198)( 12,199)( 13,200)( 14,196)( 15,197)
( 16,191)( 17,192)( 18,193)( 19,194)( 20,195)( 21,189)( 22,190)( 23,186)
( 24,187)( 25,188)( 26,157)( 27,158)( 28,159)( 29,160)( 30,156)( 31,155)
( 32,151)( 33,152)( 34,153)( 35,154)( 36,173)( 37,174)( 38,175)( 39,171)
( 40,172)( 41,166)( 42,167)( 43,168)( 44,169)( 45,170)( 46,164)( 47,165)
( 48,161)( 49,162)( 50,163)( 51,132)( 52,133)( 53,134)( 54,135)( 55,131)
( 56,130)( 57,126)( 58,127)( 59,128)( 60,129)( 61,148)( 62,149)( 63,150)
( 64,146)( 65,147)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,139)
( 72,140)( 73,136)( 74,137)( 75,138)( 76,232)( 77,233)( 78,234)( 79,235)
( 80,231)( 81,230)( 82,226)( 83,227)( 84,228)( 85,229)( 86,248)( 87,249)
( 88,250)( 89,246)( 90,247)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)
( 96,239)( 97,240)( 98,236)( 99,237)(100,238)(101,207)(102,208)(103,209)
(104,210)(105,206)(106,205)(107,201)(108,202)(109,203)(110,204)(111,223)
(112,224)(113,225)(114,221)(115,222)(116,216)(117,217)(118,218)(119,219)
(120,220)(121,214)(122,215)(123,211)(124,212)(125,213)(251,307)(252,308)
(253,309)(254,310)(255,306)(256,305)(257,301)(258,302)(259,303)(260,304)
(261,323)(262,324)(263,325)(264,321)(265,322)(266,316)(267,317)(268,318)
(269,319)(270,320)(271,314)(272,315)(273,311)(274,312)(275,313)(276,282)
(277,283)(278,284)(279,285)(280,281)(286,298)(287,299)(288,300)(289,296)
(290,297)(326,357)(327,358)(328,359)(329,360)(330,356)(331,355)(332,351)
(333,352)(334,353)(335,354)(336,373)(337,374)(338,375)(339,371)(340,372)
(341,366)(342,367)(343,368)(344,369)(345,370)(346,364)(347,365)(348,361)
(349,362)(350,363);
s2 := 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)( 27, 30)( 28, 29)( 31, 46)
( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)
( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)
( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)
( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)
( 90, 92)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)
(111,116)(112,120)(113,119)(114,118)(115,117)(127,130)(128,129)(131,146)
(132,150)(133,149)(134,148)(135,147)(136,141)(137,145)(138,144)(139,143)
(140,142)(152,155)(153,154)(156,171)(157,175)(158,174)(159,173)(160,172)
(161,166)(162,170)(163,169)(164,168)(165,167)(177,180)(178,179)(181,196)
(182,200)(183,199)(184,198)(185,197)(186,191)(187,195)(188,194)(189,193)
(190,192)(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)
(211,216)(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)
(232,250)(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)
(240,242)(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)
(261,266)(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)
(282,300)(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)
(290,292)(302,305)(303,304)(306,321)(307,325)(308,324)(309,323)(310,322)
(311,316)(312,320)(313,319)(314,318)(315,317)(327,330)(328,329)(331,346)
(332,350)(333,349)(334,348)(335,347)(336,341)(337,345)(338,344)(339,343)
(340,342)(352,355)(353,354)(356,371)(357,375)(358,374)(359,373)(360,372)
(361,366)(362,370)(363,369)(364,368)(365,367);
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*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*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 >;

References : None.
to this polytope