Polytope of Type {30,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,10}*1500e
if this polytope has a name.
Group : SmallGroup(1500,72)
Rank : 3
Schlafli Type : {30,10}
Number of vertices, edges, etc : 75, 375, 25
Order of s₀s₁s₂ : 15
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {10,10}*500
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope