Polytope of Type {4,10,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,10,3}*1200
Also Known As : {{4,10|2},{10,3}6}. if this polytope has another name.
Group : SmallGroup(1200,522)
Rank : 4
Schlafli Type : {4,10,3}
Number of vertices, edges, etc : 4, 100, 75, 15
Order of s0s1s2s3 : 12
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 : {2,10,3}*600
25-fold quotients : {4,2,3}*48
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)( 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)
(151,226)(152,230)(153,229)(154,228)(155,227)(156,246)(157,250)(158,249)
(159,248)(160,247)(161,241)(162,245)(163,244)(164,243)(165,242)(166,236)
(167,240)(168,239)(169,238)(170,237)(171,231)(172,235)(173,234)(174,233)
(175,232)(176,251)(177,255)(178,254)(179,253)(180,252)(181,271)(182,275)
(183,274)(184,273)(185,272)(186,266)(187,270)(188,269)(189,268)(190,267)
(191,261)(192,265)(193,264)(194,263)(195,262)(196,256)(197,260)(198,259)
(199,258)(200,257)(201,276)(202,280)(203,279)(204,278)(205,277)(206,296)
(207,300)(208,299)(209,298)(210,297)(211,291)(212,295)(213,294)(214,293)
(215,292)(216,286)(217,290)(218,289)(219,288)(220,287)(221,281)(222,285)
(223,284)(224,283)(225,282);;
s2 := ( 1, 2)( 3, 5)( 6, 8)( 9, 10)( 11, 14)( 12, 13)( 16, 20)( 17, 19)
( 22, 25)( 23, 24)( 26, 52)( 27, 51)( 28, 55)( 29, 54)( 30, 53)( 31, 58)
( 32, 57)( 33, 56)( 34, 60)( 35, 59)( 36, 64)( 37, 63)( 38, 62)( 39, 61)
( 40, 65)( 41, 70)( 42, 69)( 43, 68)( 44, 67)( 45, 66)( 46, 71)( 47, 75)
( 48, 74)( 49, 73)( 50, 72)( 76, 77)( 78, 80)( 81, 83)( 84, 85)( 86, 89)
( 87, 88)( 91, 95)( 92, 94)( 97,100)( 98, 99)(101,127)(102,126)(103,130)
(104,129)(105,128)(106,133)(107,132)(108,131)(109,135)(110,134)(111,139)
(112,138)(113,137)(114,136)(115,140)(116,145)(117,144)(118,143)(119,142)
(120,141)(121,146)(122,150)(123,149)(124,148)(125,147)(151,152)(153,155)
(156,158)(159,160)(161,164)(162,163)(166,170)(167,169)(172,175)(173,174)
(176,202)(177,201)(178,205)(179,204)(180,203)(181,208)(182,207)(183,206)
(184,210)(185,209)(186,214)(187,213)(188,212)(189,211)(190,215)(191,220)
(192,219)(193,218)(194,217)(195,216)(196,221)(197,225)(198,224)(199,223)
(200,222)(226,227)(228,230)(231,233)(234,235)(236,239)(237,238)(241,245)
(242,244)(247,250)(248,249)(251,277)(252,276)(253,280)(254,279)(255,278)
(256,283)(257,282)(258,281)(259,285)(260,284)(261,289)(262,288)(263,287)
(264,286)(265,290)(266,295)(267,294)(268,293)(269,292)(270,291)(271,296)
(272,300)(273,299)(274,298)(275,297);;
s3 := ( 1, 26)( 2, 32)( 3, 38)( 4, 44)( 5, 50)( 6, 46)( 7, 27)( 8, 33)
( 9, 39)( 10, 45)( 11, 41)( 12, 47)( 13, 28)( 14, 34)( 15, 40)( 16, 36)
( 17, 42)( 18, 48)( 19, 29)( 20, 35)( 21, 31)( 22, 37)( 23, 43)( 24, 49)
( 25, 30)( 52, 57)( 53, 63)( 54, 69)( 55, 75)( 56, 71)( 59, 64)( 60, 70)
( 61, 66)( 62, 72)( 68, 73)( 76,101)( 77,107)( 78,113)( 79,119)( 80,125)
( 81,121)( 82,102)( 83,108)( 84,114)( 85,120)( 86,116)( 87,122)( 88,103)
( 89,109)( 90,115)( 91,111)( 92,117)( 93,123)( 94,104)( 95,110)( 96,106)
( 97,112)( 98,118)( 99,124)(100,105)(127,132)(128,138)(129,144)(130,150)
(131,146)(134,139)(135,145)(136,141)(137,147)(143,148)(151,176)(152,182)
(153,188)(154,194)(155,200)(156,196)(157,177)(158,183)(159,189)(160,195)
(161,191)(162,197)(163,178)(164,184)(165,190)(166,186)(167,192)(168,198)
(169,179)(170,185)(171,181)(172,187)(173,193)(174,199)(175,180)(202,207)
(203,213)(204,219)(205,225)(206,221)(209,214)(210,220)(211,216)(212,222)
(218,223)(226,251)(227,257)(228,263)(229,269)(230,275)(231,271)(232,252)
(233,258)(234,264)(235,270)(236,266)(237,272)(238,253)(239,259)(240,265)
(241,261)(242,267)(243,273)(244,254)(245,260)(246,256)(247,262)(248,268)
(249,274)(250,255)(277,282)(278,288)(279,294)(280,300)(281,296)(284,289)
(285,295)(286,291)(287,297)(293,298);;
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*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)( 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)(151,226)(152,230)(153,229)(154,228)(155,227)(156,246)(157,250)
(158,249)(159,248)(160,247)(161,241)(162,245)(163,244)(164,243)(165,242)
(166,236)(167,240)(168,239)(169,238)(170,237)(171,231)(172,235)(173,234)
(174,233)(175,232)(176,251)(177,255)(178,254)(179,253)(180,252)(181,271)
(182,275)(183,274)(184,273)(185,272)(186,266)(187,270)(188,269)(189,268)
(190,267)(191,261)(192,265)(193,264)(194,263)(195,262)(196,256)(197,260)
(198,259)(199,258)(200,257)(201,276)(202,280)(203,279)(204,278)(205,277)
(206,296)(207,300)(208,299)(209,298)(210,297)(211,291)(212,295)(213,294)
(214,293)(215,292)(216,286)(217,290)(218,289)(219,288)(220,287)(221,281)
(222,285)(223,284)(224,283)(225,282);
s2 := Sym(300)!( 1, 2)( 3, 5)( 6, 8)( 9, 10)( 11, 14)( 12, 13)( 16, 20)
( 17, 19)( 22, 25)( 23, 24)( 26, 52)( 27, 51)( 28, 55)( 29, 54)( 30, 53)
( 31, 58)( 32, 57)( 33, 56)( 34, 60)( 35, 59)( 36, 64)( 37, 63)( 38, 62)
( 39, 61)( 40, 65)( 41, 70)( 42, 69)( 43, 68)( 44, 67)( 45, 66)( 46, 71)
( 47, 75)( 48, 74)( 49, 73)( 50, 72)( 76, 77)( 78, 80)( 81, 83)( 84, 85)
( 86, 89)( 87, 88)( 91, 95)( 92, 94)( 97,100)( 98, 99)(101,127)(102,126)
(103,130)(104,129)(105,128)(106,133)(107,132)(108,131)(109,135)(110,134)
(111,139)(112,138)(113,137)(114,136)(115,140)(116,145)(117,144)(118,143)
(119,142)(120,141)(121,146)(122,150)(123,149)(124,148)(125,147)(151,152)
(153,155)(156,158)(159,160)(161,164)(162,163)(166,170)(167,169)(172,175)
(173,174)(176,202)(177,201)(178,205)(179,204)(180,203)(181,208)(182,207)
(183,206)(184,210)(185,209)(186,214)(187,213)(188,212)(189,211)(190,215)
(191,220)(192,219)(193,218)(194,217)(195,216)(196,221)(197,225)(198,224)
(199,223)(200,222)(226,227)(228,230)(231,233)(234,235)(236,239)(237,238)
(241,245)(242,244)(247,250)(248,249)(251,277)(252,276)(253,280)(254,279)
(255,278)(256,283)(257,282)(258,281)(259,285)(260,284)(261,289)(262,288)
(263,287)(264,286)(265,290)(266,295)(267,294)(268,293)(269,292)(270,291)
(271,296)(272,300)(273,299)(274,298)(275,297);
s3 := Sym(300)!( 1, 26)( 2, 32)( 3, 38)( 4, 44)( 5, 50)( 6, 46)( 7, 27)
( 8, 33)( 9, 39)( 10, 45)( 11, 41)( 12, 47)( 13, 28)( 14, 34)( 15, 40)
( 16, 36)( 17, 42)( 18, 48)( 19, 29)( 20, 35)( 21, 31)( 22, 37)( 23, 43)
( 24, 49)( 25, 30)( 52, 57)( 53, 63)( 54, 69)( 55, 75)( 56, 71)( 59, 64)
( 60, 70)( 61, 66)( 62, 72)( 68, 73)( 76,101)( 77,107)( 78,113)( 79,119)
( 80,125)( 81,121)( 82,102)( 83,108)( 84,114)( 85,120)( 86,116)( 87,122)
( 88,103)( 89,109)( 90,115)( 91,111)( 92,117)( 93,123)( 94,104)( 95,110)
( 96,106)( 97,112)( 98,118)( 99,124)(100,105)(127,132)(128,138)(129,144)
(130,150)(131,146)(134,139)(135,145)(136,141)(137,147)(143,148)(151,176)
(152,182)(153,188)(154,194)(155,200)(156,196)(157,177)(158,183)(159,189)
(160,195)(161,191)(162,197)(163,178)(164,184)(165,190)(166,186)(167,192)
(168,198)(169,179)(170,185)(171,181)(172,187)(173,193)(174,199)(175,180)
(202,207)(203,213)(204,219)(205,225)(206,221)(209,214)(210,220)(211,216)
(212,222)(218,223)(226,251)(227,257)(228,263)(229,269)(230,275)(231,271)
(232,252)(233,258)(234,264)(235,270)(236,266)(237,272)(238,253)(239,259)
(240,265)(241,261)(242,267)(243,273)(244,254)(245,260)(246,256)(247,262)
(248,268)(249,274)(250,255)(277,282)(278,288)(279,294)(280,300)(281,296)
(284,289)(285,295)(286,291)(287,297)(293,298);
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,
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope