Polytope of Type {4,6,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,20}*960b
if this polytope has a name.
Group : SmallGroup(960,10952)
Rank : 4
Schlafli Type : {4,6,20}
Number of vertices, edges, etc : 4, 12, 60, 20
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,6,20,2} of size 1920
Vertex Figure Of :
{2,4,6,20} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,6,10}*480b
5-fold quotients : {4,6,4}*192c
10-fold quotients : {4,6,2}*96c
20-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,6,40}*1920b, {4,12,20}*1920b, {4,12,20}*1920c, {4,6,20}*1920a
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240);;
s1 := ( 2, 3)( 6, 7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)( 23, 42)
( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)( 31, 50)
( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)( 39, 58)
( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)( 90,111)
( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)( 98,119)
( 99,118)(100,120)(122,123)(126,127)(130,131)(134,135)(138,139)(141,161)
(142,163)(143,162)(144,164)(145,165)(146,167)(147,166)(148,168)(149,169)
(150,171)(151,170)(152,172)(153,173)(154,175)(155,174)(156,176)(157,177)
(158,179)(159,178)(160,180)(182,183)(186,187)(190,191)(194,195)(198,199)
(201,221)(202,223)(203,222)(204,224)(205,225)(206,227)(207,226)(208,228)
(209,229)(210,231)(211,230)(212,232)(213,233)(214,235)(215,234)(216,236)
(217,237)(218,239)(219,238)(220,240);;
s2 := ( 1, 41)( 2, 44)( 3, 43)( 4, 42)( 5, 57)( 6, 60)( 7, 59)( 8, 58)
( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 49)( 14, 52)( 15, 51)( 16, 50)
( 17, 45)( 18, 48)( 19, 47)( 20, 46)( 22, 24)( 25, 37)( 26, 40)( 27, 39)
( 28, 38)( 29, 33)( 30, 36)( 31, 35)( 32, 34)( 61,101)( 62,104)( 63,103)
( 64,102)( 65,117)( 66,120)( 67,119)( 68,118)( 69,113)( 70,116)( 71,115)
( 72,114)( 73,109)( 74,112)( 75,111)( 76,110)( 77,105)( 78,108)( 79,107)
( 80,106)( 82, 84)( 85, 97)( 86,100)( 87, 99)( 88, 98)( 89, 93)( 90, 96)
( 91, 95)( 92, 94)(121,221)(122,224)(123,223)(124,222)(125,237)(126,240)
(127,239)(128,238)(129,233)(130,236)(131,235)(132,234)(133,229)(134,232)
(135,231)(136,230)(137,225)(138,228)(139,227)(140,226)(141,201)(142,204)
(143,203)(144,202)(145,217)(146,220)(147,219)(148,218)(149,213)(150,216)
(151,215)(152,214)(153,209)(154,212)(155,211)(156,210)(157,205)(158,208)
(159,207)(160,206)(161,181)(162,184)(163,183)(164,182)(165,197)(166,200)
(167,199)(168,198)(169,193)(170,196)(171,195)(172,194)(173,189)(174,192)
(175,191)(176,190)(177,185)(178,188)(179,187)(180,186);;
s3 := ( 1,125)( 2,126)( 3,127)( 4,128)( 5,121)( 6,122)( 7,123)( 8,124)
( 9,137)( 10,138)( 11,139)( 12,140)( 13,133)( 14,134)( 15,135)( 16,136)
( 17,129)( 18,130)( 19,131)( 20,132)( 21,145)( 22,146)( 23,147)( 24,148)
( 25,141)( 26,142)( 27,143)( 28,144)( 29,157)( 30,158)( 31,159)( 32,160)
( 33,153)( 34,154)( 35,155)( 36,156)( 37,149)( 38,150)( 39,151)( 40,152)
( 41,165)( 42,166)( 43,167)( 44,168)( 45,161)( 46,162)( 47,163)( 48,164)
( 49,177)( 50,178)( 51,179)( 52,180)( 53,173)( 54,174)( 55,175)( 56,176)
( 57,169)( 58,170)( 59,171)( 60,172)( 61,185)( 62,186)( 63,187)( 64,188)
( 65,181)( 66,182)( 67,183)( 68,184)( 69,197)( 70,198)( 71,199)( 72,200)
( 73,193)( 74,194)( 75,195)( 76,196)( 77,189)( 78,190)( 79,191)( 80,192)
( 81,205)( 82,206)( 83,207)( 84,208)( 85,201)( 86,202)( 87,203)( 88,204)
( 89,217)( 90,218)( 91,219)( 92,220)( 93,213)( 94,214)( 95,215)( 96,216)
( 97,209)( 98,210)( 99,211)(100,212)(101,225)(102,226)(103,227)(104,228)
(105,221)(106,222)(107,223)(108,224)(109,237)(110,238)(111,239)(112,240)
(113,233)(114,234)(115,235)(116,236)(117,229)(118,230)(119,231)(120,232);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s2*s1*s0*s1*s2*s0*s1,
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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(240)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240);
s1 := Sym(240)!( 2, 3)( 6, 7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)
( 23, 42)( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)
( 31, 50)( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)
( 39, 58)( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)
( 82,103)( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)
( 90,111)( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)
( 98,119)( 99,118)(100,120)(122,123)(126,127)(130,131)(134,135)(138,139)
(141,161)(142,163)(143,162)(144,164)(145,165)(146,167)(147,166)(148,168)
(149,169)(150,171)(151,170)(152,172)(153,173)(154,175)(155,174)(156,176)
(157,177)(158,179)(159,178)(160,180)(182,183)(186,187)(190,191)(194,195)
(198,199)(201,221)(202,223)(203,222)(204,224)(205,225)(206,227)(207,226)
(208,228)(209,229)(210,231)(211,230)(212,232)(213,233)(214,235)(215,234)
(216,236)(217,237)(218,239)(219,238)(220,240);
s2 := Sym(240)!( 1, 41)( 2, 44)( 3, 43)( 4, 42)( 5, 57)( 6, 60)( 7, 59)
( 8, 58)( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 49)( 14, 52)( 15, 51)
( 16, 50)( 17, 45)( 18, 48)( 19, 47)( 20, 46)( 22, 24)( 25, 37)( 26, 40)
( 27, 39)( 28, 38)( 29, 33)( 30, 36)( 31, 35)( 32, 34)( 61,101)( 62,104)
( 63,103)( 64,102)( 65,117)( 66,120)( 67,119)( 68,118)( 69,113)( 70,116)
( 71,115)( 72,114)( 73,109)( 74,112)( 75,111)( 76,110)( 77,105)( 78,108)
( 79,107)( 80,106)( 82, 84)( 85, 97)( 86,100)( 87, 99)( 88, 98)( 89, 93)
( 90, 96)( 91, 95)( 92, 94)(121,221)(122,224)(123,223)(124,222)(125,237)
(126,240)(127,239)(128,238)(129,233)(130,236)(131,235)(132,234)(133,229)
(134,232)(135,231)(136,230)(137,225)(138,228)(139,227)(140,226)(141,201)
(142,204)(143,203)(144,202)(145,217)(146,220)(147,219)(148,218)(149,213)
(150,216)(151,215)(152,214)(153,209)(154,212)(155,211)(156,210)(157,205)
(158,208)(159,207)(160,206)(161,181)(162,184)(163,183)(164,182)(165,197)
(166,200)(167,199)(168,198)(169,193)(170,196)(171,195)(172,194)(173,189)
(174,192)(175,191)(176,190)(177,185)(178,188)(179,187)(180,186);
s3 := Sym(240)!( 1,125)( 2,126)( 3,127)( 4,128)( 5,121)( 6,122)( 7,123)
( 8,124)( 9,137)( 10,138)( 11,139)( 12,140)( 13,133)( 14,134)( 15,135)
( 16,136)( 17,129)( 18,130)( 19,131)( 20,132)( 21,145)( 22,146)( 23,147)
( 24,148)( 25,141)( 26,142)( 27,143)( 28,144)( 29,157)( 30,158)( 31,159)
( 32,160)( 33,153)( 34,154)( 35,155)( 36,156)( 37,149)( 38,150)( 39,151)
( 40,152)( 41,165)( 42,166)( 43,167)( 44,168)( 45,161)( 46,162)( 47,163)
( 48,164)( 49,177)( 50,178)( 51,179)( 52,180)( 53,173)( 54,174)( 55,175)
( 56,176)( 57,169)( 58,170)( 59,171)( 60,172)( 61,185)( 62,186)( 63,187)
( 64,188)( 65,181)( 66,182)( 67,183)( 68,184)( 69,197)( 70,198)( 71,199)
( 72,200)( 73,193)( 74,194)( 75,195)( 76,196)( 77,189)( 78,190)( 79,191)
( 80,192)( 81,205)( 82,206)( 83,207)( 84,208)( 85,201)( 86,202)( 87,203)
( 88,204)( 89,217)( 90,218)( 91,219)( 92,220)( 93,213)( 94,214)( 95,215)
( 96,216)( 97,209)( 98,210)( 99,211)(100,212)(101,225)(102,226)(103,227)
(104,228)(105,221)(106,222)(107,223)(108,224)(109,237)(110,238)(111,239)
(112,240)(113,233)(114,234)(115,235)(116,236)(117,229)(118,230)(119,231)
(120,232);
poly := sub<Sym(240)|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, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s2*s1*s0*s1*s2*s0*s1, 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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope