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Polytope of Type {15,10,4}

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