Polytope of Type {4,10,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10,15}*1200
if this polytope has a name.
Group : SmallGroup(1200,856)
Rank : 4
Schlafli Type : {4,10,15}
Number of vertices, edges, etc : 4, 20, 75, 15
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
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) :
2-fold quotients : {2,10,15}*600
3-fold quotients : {4,10,5}*400
5-fold quotients : {4,2,15}*240
6-fold quotients : {2,10,5}*200
10-fold quotients : {2,2,15}*120
15-fold quotients : {4,2,5}*80
25-fold quotients : {4,2,3}*48
30-fold quotients : {2,2,5}*40
50-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,151)( 2,152)( 3,153)( 4,154)( 5,155)( 6,156)( 7,157)( 8,158)
( 9,159)( 10,160)( 11,161)( 12,162)( 13,163)( 14,164)( 15,165)( 16,166)
( 17,167)( 18,168)( 19,169)( 20,170)( 21,171)( 22,172)( 23,173)( 24,174)
( 25,175)( 26,176)( 27,177)( 28,178)( 29,179)( 30,180)( 31,181)( 32,182)
( 33,183)( 34,184)( 35,185)( 36,186)( 37,187)( 38,188)( 39,189)( 40,190)
( 41,191)( 42,192)( 43,193)( 44,194)( 45,195)( 46,196)( 47,197)( 48,198)
( 49,199)( 50,200)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)( 56,206)
( 57,207)( 58,208)( 59,209)( 60,210)( 61,211)( 62,212)( 63,213)( 64,214)
( 65,215)( 66,216)( 67,217)( 68,218)( 69,219)( 70,220)( 71,221)( 72,222)
( 73,223)( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)( 80,230)
( 81,231)( 82,232)( 83,233)( 84,234)( 85,235)( 86,236)( 87,237)( 88,238)
( 89,239)( 90,240)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)( 96,246)
( 97,247)( 98,248)( 99,249)(100,250)(101,251)(102,252)(103,253)(104,254)
(105,255)(106,256)(107,257)(108,258)(109,259)(110,260)(111,261)(112,262)
(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)(120,270)
(121,271)(122,272)(123,273)(124,274)(125,275)(126,276)(127,277)(128,278)
(129,279)(130,280)(131,281)(132,282)(133,283)(134,284)(135,285)(136,286)
(137,287)(138,288)(139,289)(140,290)(141,291)(142,292)(143,293)(144,294)
(145,295)(146,296)(147,297)(148,298)(149,299)(150,300);;
s1 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)( 78, 79)
( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)( 98, 99)
(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)(118,119)
(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)
(142,145)(143,144)(147,150)(148,149)(151,226)(152,230)(153,229)(154,228)
(155,227)(156,231)(157,235)(158,234)(159,233)(160,232)(161,236)(162,240)
(163,239)(164,238)(165,237)(166,241)(167,245)(168,244)(169,243)(170,242)
(171,246)(172,250)(173,249)(174,248)(175,247)(176,251)(177,255)(178,254)
(179,253)(180,252)(181,256)(182,260)(183,259)(184,258)(185,257)(186,261)
(187,265)(188,264)(189,263)(190,262)(191,266)(192,270)(193,269)(194,268)
(195,267)(196,271)(197,275)(198,274)(199,273)(200,272)(201,276)(202,280)
(203,279)(204,278)(205,277)(206,281)(207,285)(208,284)(209,283)(210,282)
(211,286)(212,290)(213,289)(214,288)(215,287)(216,291)(217,295)(218,294)
(219,293)(220,292)(221,296)(222,300)(223,299)(224,298)(225,297);;
s2 := ( 1, 2)( 3, 5)( 6, 22)( 7, 21)( 8, 25)( 9, 24)( 10, 23)( 11, 17)
( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 52)( 27, 51)( 28, 55)( 29, 54)
( 30, 53)( 31, 72)( 32, 71)( 33, 75)( 34, 74)( 35, 73)( 36, 67)( 37, 66)
( 38, 70)( 39, 69)( 40, 68)( 41, 62)( 42, 61)( 43, 65)( 44, 64)( 45, 63)
( 46, 57)( 47, 56)( 48, 60)( 49, 59)( 50, 58)( 76, 77)( 78, 80)( 81, 97)
( 82, 96)( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)( 89, 94)
( 90, 93)(101,127)(102,126)(103,130)(104,129)(105,128)(106,147)(107,146)
(108,150)(109,149)(110,148)(111,142)(112,141)(113,145)(114,144)(115,143)
(116,137)(117,136)(118,140)(119,139)(120,138)(121,132)(122,131)(123,135)
(124,134)(125,133)(151,152)(153,155)(156,172)(157,171)(158,175)(159,174)
(160,173)(161,167)(162,166)(163,170)(164,169)(165,168)(176,202)(177,201)
(178,205)(179,204)(180,203)(181,222)(182,221)(183,225)(184,224)(185,223)
(186,217)(187,216)(188,220)(189,219)(190,218)(191,212)(192,211)(193,215)
(194,214)(195,213)(196,207)(197,206)(198,210)(199,209)(200,208)(226,227)
(228,230)(231,247)(232,246)(233,250)(234,249)(235,248)(236,242)(237,241)
(238,245)(239,244)(240,243)(251,277)(252,276)(253,280)(254,279)(255,278)
(256,297)(257,296)(258,300)(259,299)(260,298)(261,292)(262,291)(263,295)
(264,294)(265,293)(266,287)(267,286)(268,290)(269,289)(270,288)(271,282)
(272,281)(273,285)(274,284)(275,283);;
s3 := ( 1, 31)( 2, 35)( 3, 34)( 4, 33)( 5, 32)( 6, 26)( 7, 30)( 8, 29)
( 9, 28)( 10, 27)( 11, 46)( 12, 50)( 13, 49)( 14, 48)( 15, 47)( 16, 41)
( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 36)( 22, 40)( 23, 39)( 24, 38)
( 25, 37)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 71)( 62, 75)
( 63, 74)( 64, 73)( 65, 72)( 67, 70)( 68, 69)( 76,106)( 77,110)( 78,109)
( 79,108)( 80,107)( 81,101)( 82,105)( 83,104)( 84,103)( 85,102)( 86,121)
( 87,125)( 88,124)( 89,123)( 90,122)( 91,116)( 92,120)( 93,119)( 94,118)
( 95,117)( 96,111)( 97,115)( 98,114)( 99,113)(100,112)(126,131)(127,135)
(128,134)(129,133)(130,132)(136,146)(137,150)(138,149)(139,148)(140,147)
(142,145)(143,144)(151,181)(152,185)(153,184)(154,183)(155,182)(156,176)
(157,180)(158,179)(159,178)(160,177)(161,196)(162,200)(163,199)(164,198)
(165,197)(166,191)(167,195)(168,194)(169,193)(170,192)(171,186)(172,190)
(173,189)(174,188)(175,187)(201,206)(202,210)(203,209)(204,208)(205,207)
(211,221)(212,225)(213,224)(214,223)(215,222)(217,220)(218,219)(226,256)
(227,260)(228,259)(229,258)(230,257)(231,251)(232,255)(233,254)(234,253)
(235,252)(236,271)(237,275)(238,274)(239,273)(240,272)(241,266)(242,270)
(243,269)(244,268)(245,267)(246,261)(247,265)(248,264)(249,263)(250,262)
(276,281)(277,285)(278,284)(279,283)(280,282)(286,296)(287,300)(288,299)
(289,298)(290,297)(292,295)(293,294);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(300)!( 1,151)( 2,152)( 3,153)( 4,154)( 5,155)( 6,156)( 7,157)
( 8,158)( 9,159)( 10,160)( 11,161)( 12,162)( 13,163)( 14,164)( 15,165)
( 16,166)( 17,167)( 18,168)( 19,169)( 20,170)( 21,171)( 22,172)( 23,173)
( 24,174)( 25,175)( 26,176)( 27,177)( 28,178)( 29,179)( 30,180)( 31,181)
( 32,182)( 33,183)( 34,184)( 35,185)( 36,186)( 37,187)( 38,188)( 39,189)
( 40,190)( 41,191)( 42,192)( 43,193)( 44,194)( 45,195)( 46,196)( 47,197)
( 48,198)( 49,199)( 50,200)( 51,201)( 52,202)( 53,203)( 54,204)( 55,205)
( 56,206)( 57,207)( 58,208)( 59,209)( 60,210)( 61,211)( 62,212)( 63,213)
( 64,214)( 65,215)( 66,216)( 67,217)( 68,218)( 69,219)( 70,220)( 71,221)
( 72,222)( 73,223)( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)
( 80,230)( 81,231)( 82,232)( 83,233)( 84,234)( 85,235)( 86,236)( 87,237)
( 88,238)( 89,239)( 90,240)( 91,241)( 92,242)( 93,243)( 94,244)( 95,245)
( 96,246)( 97,247)( 98,248)( 99,249)(100,250)(101,251)(102,252)(103,253)
(104,254)(105,255)(106,256)(107,257)(108,258)(109,259)(110,260)(111,261)
(112,262)(113,263)(114,264)(115,265)(116,266)(117,267)(118,268)(119,269)
(120,270)(121,271)(122,272)(123,273)(124,274)(125,275)(126,276)(127,277)
(128,278)(129,279)(130,280)(131,281)(132,282)(133,283)(134,284)(135,285)
(136,286)(137,287)(138,288)(139,289)(140,290)(141,291)(142,292)(143,293)
(144,294)(145,295)(146,296)(147,297)(148,298)(149,299)(150,300);
s1 := Sym(300)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 62, 65)( 63, 64)( 67, 70)( 68, 69)( 72, 75)( 73, 74)( 77, 80)
( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 92, 95)( 93, 94)( 97,100)
( 98, 99)(102,105)(103,104)(107,110)(108,109)(112,115)(113,114)(117,120)
(118,119)(122,125)(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)
(138,139)(142,145)(143,144)(147,150)(148,149)(151,226)(152,230)(153,229)
(154,228)(155,227)(156,231)(157,235)(158,234)(159,233)(160,232)(161,236)
(162,240)(163,239)(164,238)(165,237)(166,241)(167,245)(168,244)(169,243)
(170,242)(171,246)(172,250)(173,249)(174,248)(175,247)(176,251)(177,255)
(178,254)(179,253)(180,252)(181,256)(182,260)(183,259)(184,258)(185,257)
(186,261)(187,265)(188,264)(189,263)(190,262)(191,266)(192,270)(193,269)
(194,268)(195,267)(196,271)(197,275)(198,274)(199,273)(200,272)(201,276)
(202,280)(203,279)(204,278)(205,277)(206,281)(207,285)(208,284)(209,283)
(210,282)(211,286)(212,290)(213,289)(214,288)(215,287)(216,291)(217,295)
(218,294)(219,293)(220,292)(221,296)(222,300)(223,299)(224,298)(225,297);
s2 := Sym(300)!( 1, 2)( 3, 5)( 6, 22)( 7, 21)( 8, 25)( 9, 24)( 10, 23)
( 11, 17)( 12, 16)( 13, 20)( 14, 19)( 15, 18)( 26, 52)( 27, 51)( 28, 55)
( 29, 54)( 30, 53)( 31, 72)( 32, 71)( 33, 75)( 34, 74)( 35, 73)( 36, 67)
( 37, 66)( 38, 70)( 39, 69)( 40, 68)( 41, 62)( 42, 61)( 43, 65)( 44, 64)
( 45, 63)( 46, 57)( 47, 56)( 48, 60)( 49, 59)( 50, 58)( 76, 77)( 78, 80)
( 81, 97)( 82, 96)( 83,100)( 84, 99)( 85, 98)( 86, 92)( 87, 91)( 88, 95)
( 89, 94)( 90, 93)(101,127)(102,126)(103,130)(104,129)(105,128)(106,147)
(107,146)(108,150)(109,149)(110,148)(111,142)(112,141)(113,145)(114,144)
(115,143)(116,137)(117,136)(118,140)(119,139)(120,138)(121,132)(122,131)
(123,135)(124,134)(125,133)(151,152)(153,155)(156,172)(157,171)(158,175)
(159,174)(160,173)(161,167)(162,166)(163,170)(164,169)(165,168)(176,202)
(177,201)(178,205)(179,204)(180,203)(181,222)(182,221)(183,225)(184,224)
(185,223)(186,217)(187,216)(188,220)(189,219)(190,218)(191,212)(192,211)
(193,215)(194,214)(195,213)(196,207)(197,206)(198,210)(199,209)(200,208)
(226,227)(228,230)(231,247)(232,246)(233,250)(234,249)(235,248)(236,242)
(237,241)(238,245)(239,244)(240,243)(251,277)(252,276)(253,280)(254,279)
(255,278)(256,297)(257,296)(258,300)(259,299)(260,298)(261,292)(262,291)
(263,295)(264,294)(265,293)(266,287)(267,286)(268,290)(269,289)(270,288)
(271,282)(272,281)(273,285)(274,284)(275,283);
s3 := Sym(300)!( 1, 31)( 2, 35)( 3, 34)( 4, 33)( 5, 32)( 6, 26)( 7, 30)
( 8, 29)( 9, 28)( 10, 27)( 11, 46)( 12, 50)( 13, 49)( 14, 48)( 15, 47)
( 16, 41)( 17, 45)( 18, 44)( 19, 43)( 20, 42)( 21, 36)( 22, 40)( 23, 39)
( 24, 38)( 25, 37)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61, 71)
( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 67, 70)( 68, 69)( 76,106)( 77,110)
( 78,109)( 79,108)( 80,107)( 81,101)( 82,105)( 83,104)( 84,103)( 85,102)
( 86,121)( 87,125)( 88,124)( 89,123)( 90,122)( 91,116)( 92,120)( 93,119)
( 94,118)( 95,117)( 96,111)( 97,115)( 98,114)( 99,113)(100,112)(126,131)
(127,135)(128,134)(129,133)(130,132)(136,146)(137,150)(138,149)(139,148)
(140,147)(142,145)(143,144)(151,181)(152,185)(153,184)(154,183)(155,182)
(156,176)(157,180)(158,179)(159,178)(160,177)(161,196)(162,200)(163,199)
(164,198)(165,197)(166,191)(167,195)(168,194)(169,193)(170,192)(171,186)
(172,190)(173,189)(174,188)(175,187)(201,206)(202,210)(203,209)(204,208)
(205,207)(211,221)(212,225)(213,224)(214,223)(215,222)(217,220)(218,219)
(226,256)(227,260)(228,259)(229,258)(230,257)(231,251)(232,255)(233,254)
(234,253)(235,252)(236,271)(237,275)(238,274)(239,273)(240,272)(241,266)
(242,270)(243,269)(244,268)(245,267)(246,261)(247,265)(248,264)(249,263)
(250,262)(276,281)(277,285)(278,284)(279,283)(280,282)(286,296)(287,300)
(288,299)(289,298)(290,297)(292,295)(293,294);
poly := sub<Sym(300)|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,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope