Polytope of Type {20,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,6}*1440b
if this polytope has a name.
Group : SmallGroup(1440,5284)
Rank : 4
Schlafli Type : {20,6,6}
Number of vertices, edges, etc : 20, 60, 18, 6
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 : {10,6,6}*720c
3-fold quotients : {20,6,2}*480a
5-fold quotients : {4,6,6}*288b
6-fold quotients : {10,6,2}*240
9-fold quotients : {20,2,2}*160
10-fold quotients : {2,6,6}*144c
15-fold quotients : {4,6,2}*96a
18-fold quotients : {10,2,2}*80
20-fold quotients : {2,3,6}*72
30-fold quotients : {2,6,2}*48
36-fold quotients : {5,2,2}*40
45-fold quotients : {4,2,2}*32
60-fold quotients : {2,3,2}*24
90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 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)( 91,136)( 92,140)( 93,139)( 94,138)( 95,137)( 96,141)( 97,145)( 98,144)( 99,143)(100,142)(101,146)(102,150)(103,149)(104,148)(105,147)(106,151)(107,155)(108,154)(109,153)(110,152)(111,156)(112,160)(113,159)(114,158)(115,157)(116,161)(117,165)(118,164)(119,163)(120,162)(121,166)(122,170)(123,169)(124,168)(125,167)(126,171)(127,175)(128,174)(129,173)(130,172)(131,176)(132,180)(133,179)(134,178)(135,177);;
s1 := ( 1, 92)( 2, 91)( 3, 95)( 4, 94)( 5, 93)( 6,102)( 7,101)( 8,105)( 9,104)( 10,103)( 11, 97)( 12, 96)( 13,100)( 14, 99)( 15, 98)( 16,122)( 17,121)( 18,125)( 19,124)( 20,123)( 21,132)( 22,131)( 23,135)( 24,134)( 25,133)( 26,127)( 27,126)( 28,130)( 29,129)( 30,128)( 31,107)( 32,106)( 33,110)( 34,109)( 35,108)( 36,117)( 37,116)( 38,120)( 39,119)( 40,118)( 41,112)( 42,111)( 43,115)( 44,114)( 45,113)( 46,137)( 47,136)( 48,140)( 49,139)( 50,138)( 51,147)( 52,146)( 53,150)( 54,149)( 55,148)( 56,142)( 57,141)( 58,145)( 59,144)( 60,143)( 61,167)( 62,166)( 63,170)( 64,169)( 65,168)( 66,177)( 67,176)( 68,180)( 69,179)( 70,178)( 71,172)( 72,171)( 73,175)( 74,174)( 75,173)( 76,152)( 77,151)( 78,155)( 79,154)( 80,153)( 81,162)( 82,161)( 83,165)( 84,164)( 85,163)( 86,157)( 87,156)( 88,160)( 89,159)( 90,158);;
s2 := ( 1, 21)( 2, 22)( 3, 23)( 4, 24)( 5, 25)( 6, 16)( 7, 17)( 8, 18)( 9, 19)( 10, 20)( 11, 26)( 12, 27)( 13, 28)( 14, 29)( 15, 30)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 46, 66)( 47, 67)( 48, 68)( 49, 69)( 50, 70)( 51, 61)( 52, 62)( 53, 63)( 54, 64)( 55, 65)( 56, 71)( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91,111)( 92,112)( 93,113)( 94,114)( 95,115)( 96,106)( 97,107)( 98,108)( 99,109)(100,110)(101,116)(102,117)(103,118)(104,119)(105,120)(121,126)(122,127)(123,128)(124,129)(125,130)(136,156)(137,157)(138,158)(139,159)(140,160)(141,151)(142,152)(143,153)(144,154)(145,155)(146,161)(147,162)(148,163)(149,164)(150,165)(166,171)(167,172)(168,173)(169,174)(170,175);;
s3 := ( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 66, 71)( 67, 72)( 68, 73)( 69, 74)( 70, 75)( 81, 86)( 82, 87)( 83, 88)( 84, 89)( 85, 90)( 96,101)( 97,102)( 98,103)( 99,104)(100,105)(111,116)(112,117)(113,118)(114,119)(115,120)(126,131)(127,132)(128,133)(129,134)(130,135)(141,146)(142,147)(143,148)(144,149)(145,150)(156,161)(157,162)(158,163)(159,164)(160,165)(171,176)(172,177)(173,178)(174,179)(175,180);;
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*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
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*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(180)!( 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)( 91,136)( 92,140)( 93,139)( 94,138)( 95,137)( 96,141)( 97,145)( 98,144)( 99,143)(100,142)(101,146)(102,150)(103,149)(104,148)(105,147)(106,151)(107,155)(108,154)(109,153)(110,152)(111,156)(112,160)(113,159)(114,158)(115,157)(116,161)(117,165)(118,164)(119,163)(120,162)(121,166)(122,170)(123,169)(124,168)(125,167)(126,171)(127,175)(128,174)(129,173)(130,172)(131,176)(132,180)(133,179)(134,178)(135,177);
s1 := Sym(180)!( 1, 92)( 2, 91)( 3, 95)( 4, 94)( 5, 93)( 6,102)( 7,101)( 8,105)( 9,104)( 10,103)( 11, 97)( 12, 96)( 13,100)( 14, 99)( 15, 98)( 16,122)( 17,121)( 18,125)( 19,124)( 20,123)( 21,132)( 22,131)( 23,135)( 24,134)( 25,133)( 26,127)( 27,126)( 28,130)( 29,129)( 30,128)( 31,107)( 32,106)( 33,110)( 34,109)( 35,108)( 36,117)( 37,116)( 38,120)( 39,119)( 40,118)( 41,112)( 42,111)( 43,115)( 44,114)( 45,113)( 46,137)( 47,136)( 48,140)( 49,139)( 50,138)( 51,147)( 52,146)( 53,150)( 54,149)( 55,148)( 56,142)( 57,141)( 58,145)( 59,144)( 60,143)( 61,167)( 62,166)( 63,170)( 64,169)( 65,168)( 66,177)( 67,176)( 68,180)( 69,179)( 70,178)( 71,172)( 72,171)( 73,175)( 74,174)( 75,173)( 76,152)( 77,151)( 78,155)( 79,154)( 80,153)( 81,162)( 82,161)( 83,165)( 84,164)( 85,163)( 86,157)( 87,156)( 88,160)( 89,159)( 90,158);
s2 := Sym(180)!( 1, 21)( 2, 22)( 3, 23)( 4, 24)( 5, 25)( 6, 16)( 7, 17)( 8, 18)( 9, 19)( 10, 20)( 11, 26)( 12, 27)( 13, 28)( 14, 29)( 15, 30)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 46, 66)( 47, 67)( 48, 68)( 49, 69)( 50, 70)( 51, 61)( 52, 62)( 53, 63)( 54, 64)( 55, 65)( 56, 71)( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91,111)( 92,112)( 93,113)( 94,114)( 95,115)( 96,106)( 97,107)( 98,108)( 99,109)(100,110)(101,116)(102,117)(103,118)(104,119)(105,120)(121,126)(122,127)(123,128)(124,129)(125,130)(136,156)(137,157)(138,158)(139,159)(140,160)(141,151)(142,152)(143,153)(144,154)(145,155)(146,161)(147,162)(148,163)(149,164)(150,165)(166,171)(167,172)(168,173)(169,174)(170,175);
s3 := Sym(180)!( 6, 11)( 7, 12)( 8, 13)( 9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 66, 71)( 67, 72)( 68, 73)( 69, 74)( 70, 75)( 81, 86)( 82, 87)( 83, 88)( 84, 89)( 85, 90)( 96,101)( 97,102)( 98,103)( 99,104)(100,105)(111,116)(112,117)(113,118)(114,119)(115,120)(126,131)(127,132)(128,133)(129,134)(130,135)(141,146)(142,147)(143,148)(144,149)(145,150)(156,161)(157,162)(158,163)(159,164)(160,165)(171,176)(172,177)(173,178)(174,179)(175,180);
poly := sub<Sym(180)|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*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
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*s0*s1*s0*s1 >;
References : None.
to this polytope