Polytope of Type {15,10,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,10,5}*1500
if this polytope has a name.
Group : SmallGroup(1500,72)
Rank : 4
Schlafli Type : {15,10,5}
Number of vertices, edges, etc : 15, 75, 25, 5
Order of s0s1s2s3 : 15
Order of s0s1s2s3s2s1 : 10
Special Properties :
Universal
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 : {5,10,5}*500
5-fold quotients : {15,2,5}*300
15-fold quotients : {5,2,5}*100
25-fold quotients : {3,2,5}*60
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)( 2,155)( 3,154)( 4,153)( 5,152)( 6,157)( 7,156)( 8,160)
( 9,159)( 10,158)( 11,163)( 12,162)( 13,161)( 14,165)( 15,164)( 16,169)
( 17,168)( 18,167)( 19,166)( 20,170)( 21,175)( 22,174)( 23,173)( 24,172)
( 25,171)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,132)( 32,131)
( 33,135)( 34,134)( 35,133)( 36,138)( 37,137)( 38,136)( 39,140)( 40,139)
( 41,144)( 42,143)( 43,142)( 44,141)( 45,145)( 46,150)( 47,149)( 48,148)
( 49,147)( 50,146)( 51,226)( 52,230)( 53,229)( 54,228)( 55,227)( 56,232)
( 57,231)( 58,235)( 59,234)( 60,233)( 61,238)( 62,237)( 63,236)( 64,240)
( 65,239)( 66,244)( 67,243)( 68,242)( 69,241)( 70,245)( 71,250)( 72,249)
( 73,248)( 74,247)( 75,246)( 76,201)( 77,205)( 78,204)( 79,203)( 80,202)
( 81,207)( 82,206)( 83,210)( 84,209)( 85,208)( 86,213)( 87,212)( 88,211)
( 89,215)( 90,214)( 91,219)( 92,218)( 93,217)( 94,216)( 95,220)( 96,225)
( 97,224)( 98,223)( 99,222)(100,221)(101,176)(102,180)(103,179)(104,178)
(105,177)(106,182)(107,181)(108,185)(109,184)(110,183)(111,188)(112,187)
(113,186)(114,190)(115,189)(116,194)(117,193)(118,192)(119,191)(120,195)
(121,200)(122,199)(123,198)(124,197)(125,196)(251,276)(252,280)(253,279)
(254,278)(255,277)(256,282)(257,281)(258,285)(259,284)(260,283)(261,288)
(262,287)(263,286)(264,290)(265,289)(266,294)(267,293)(268,292)(269,291)
(270,295)(271,300)(272,299)(273,298)(274,297)(275,296)(301,351)(302,355)
(303,354)(304,353)(305,352)(306,357)(307,356)(308,360)(309,359)(310,358)
(311,363)(312,362)(313,361)(314,365)(315,364)(316,369)(317,368)(318,367)
(319,366)(320,370)(321,375)(322,374)(323,373)(324,372)(325,371)(327,330)
(328,329)(331,332)(333,335)(336,338)(339,340)(341,344)(342,343)(346,350)
(347,349);;
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);;
s3 := ( 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,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)( 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)( 2,155)( 3,154)( 4,153)( 5,152)( 6,157)( 7,156)
( 8,160)( 9,159)( 10,158)( 11,163)( 12,162)( 13,161)( 14,165)( 15,164)
( 16,169)( 17,168)( 18,167)( 19,166)( 20,170)( 21,175)( 22,174)( 23,173)
( 24,172)( 25,171)( 26,126)( 27,130)( 28,129)( 29,128)( 30,127)( 31,132)
( 32,131)( 33,135)( 34,134)( 35,133)( 36,138)( 37,137)( 38,136)( 39,140)
( 40,139)( 41,144)( 42,143)( 43,142)( 44,141)( 45,145)( 46,150)( 47,149)
( 48,148)( 49,147)( 50,146)( 51,226)( 52,230)( 53,229)( 54,228)( 55,227)
( 56,232)( 57,231)( 58,235)( 59,234)( 60,233)( 61,238)( 62,237)( 63,236)
( 64,240)( 65,239)( 66,244)( 67,243)( 68,242)( 69,241)( 70,245)( 71,250)
( 72,249)( 73,248)( 74,247)( 75,246)( 76,201)( 77,205)( 78,204)( 79,203)
( 80,202)( 81,207)( 82,206)( 83,210)( 84,209)( 85,208)( 86,213)( 87,212)
( 88,211)( 89,215)( 90,214)( 91,219)( 92,218)( 93,217)( 94,216)( 95,220)
( 96,225)( 97,224)( 98,223)( 99,222)(100,221)(101,176)(102,180)(103,179)
(104,178)(105,177)(106,182)(107,181)(108,185)(109,184)(110,183)(111,188)
(112,187)(113,186)(114,190)(115,189)(116,194)(117,193)(118,192)(119,191)
(120,195)(121,200)(122,199)(123,198)(124,197)(125,196)(251,276)(252,280)
(253,279)(254,278)(255,277)(256,282)(257,281)(258,285)(259,284)(260,283)
(261,288)(262,287)(263,286)(264,290)(265,289)(266,294)(267,293)(268,292)
(269,291)(270,295)(271,300)(272,299)(273,298)(274,297)(275,296)(301,351)
(302,355)(303,354)(304,353)(305,352)(306,357)(307,356)(308,360)(309,359)
(310,358)(311,363)(312,362)(313,361)(314,365)(315,364)(316,369)(317,368)
(318,367)(319,366)(320,370)(321,375)(322,374)(323,373)(324,372)(325,371)
(327,330)(328,329)(331,332)(333,335)(336,338)(339,340)(341,344)(342,343)
(346,350)(347,349);
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);
s3 := 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,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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