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