Overview
- Group
- SmallGroup(1440,5284)
- Rank
- 4
- Schläfli Type
- {6,6,20}
- Vertices, edges, …
- 6, 18, 60, 20
- Order of s0s1s2s3
- 60
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{6,6|2},{6,20|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
5-fold
6-fold
9-fold
10-fold
12-fold
15-fold
18-fold
24-fold
30-fold
36-fold
45-fold
60-fold
90-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 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);; s1 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 36)( 17, 37)( 18, 38)( 19, 39)( 20, 40)( 21, 31)( 22, 32)( 23, 33)( 24, 34)( 25, 35)( 26, 41)( 27, 42)( 28, 43)( 29, 44)( 30, 45)( 46, 51)( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 81)( 62, 82)( 63, 83)( 64, 84)( 65, 85)( 66, 76)( 67, 77)( 68, 78)( 69, 79)( 70, 80)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 91, 96)( 92, 97)( 93, 98)( 94, 99)( 95,100)(106,126)(107,127)(108,128)(109,129)(110,130)(111,121)(112,122)(113,123)(114,124)(115,125)(116,131)(117,132)(118,133)(119,134)(120,135)(136,141)(137,142)(138,143)(139,144)(140,145)(151,171)(152,172)(153,173)(154,174)(155,175)(156,166)(157,167)(158,168)(159,169)(160,170)(161,176)(162,177)(163,178)(164,179)(165,180);; s2 := ( 1, 16)( 2, 20)( 3, 19)( 4, 18)( 5, 17)( 6, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 26)( 12, 30)( 13, 29)( 14, 28)( 15, 27)( 32, 35)( 33, 34)( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 46, 61)( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 51, 66)( 52, 70)( 53, 69)( 54, 68)( 55, 67)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 77, 80)( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 91,151)( 92,155)( 93,154)( 94,153)( 95,152)( 96,156)( 97,160)( 98,159)( 99,158)(100,157)(101,161)(102,165)(103,164)(104,163)(105,162)(106,136)(107,140)(108,139)(109,138)(110,137)(111,141)(112,145)(113,144)(114,143)(115,142)(116,146)(117,150)(118,149)(119,148)(120,147)(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);; s3 := ( 1, 92)( 2, 91)( 3, 95)( 4, 94)( 5, 93)( 6, 97)( 7, 96)( 8,100)( 9, 99)( 10, 98)( 11,102)( 12,101)( 13,105)( 14,104)( 15,103)( 16,107)( 17,106)( 18,110)( 19,109)( 20,108)( 21,112)( 22,111)( 23,115)( 24,114)( 25,113)( 26,117)( 27,116)( 28,120)( 29,119)( 30,118)( 31,122)( 32,121)( 33,125)( 34,124)( 35,123)( 36,127)( 37,126)( 38,130)( 39,129)( 40,128)( 41,132)( 42,131)( 43,135)( 44,134)( 45,133)( 46,137)( 47,136)( 48,140)( 49,139)( 50,138)( 51,142)( 52,141)( 53,145)( 54,144)( 55,143)( 56,147)( 57,146)( 58,150)( 59,149)( 60,148)( 61,152)( 62,151)( 63,155)( 64,154)( 65,153)( 66,157)( 67,156)( 68,160)( 69,159)( 70,158)( 71,162)( 72,161)( 73,165)( 74,164)( 75,163)( 76,167)( 77,166)( 78,170)( 79,169)( 80,168)( 81,172)( 82,171)( 83,175)( 84,174)( 85,173)( 86,177)( 87,176)( 88,180)( 89,179)( 90,178);; 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,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(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); s1 := Sym(180)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 36)( 17, 37)( 18, 38)( 19, 39)( 20, 40)( 21, 31)( 22, 32)( 23, 33)( 24, 34)( 25, 35)( 26, 41)( 27, 42)( 28, 43)( 29, 44)( 30, 45)( 46, 51)( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 81)( 62, 82)( 63, 83)( 64, 84)( 65, 85)( 66, 76)( 67, 77)( 68, 78)( 69, 79)( 70, 80)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 91, 96)( 92, 97)( 93, 98)( 94, 99)( 95,100)(106,126)(107,127)(108,128)(109,129)(110,130)(111,121)(112,122)(113,123)(114,124)(115,125)(116,131)(117,132)(118,133)(119,134)(120,135)(136,141)(137,142)(138,143)(139,144)(140,145)(151,171)(152,172)(153,173)(154,174)(155,175)(156,166)(157,167)(158,168)(159,169)(160,170)(161,176)(162,177)(163,178)(164,179)(165,180); s2 := Sym(180)!( 1, 16)( 2, 20)( 3, 19)( 4, 18)( 5, 17)( 6, 21)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 26)( 12, 30)( 13, 29)( 14, 28)( 15, 27)( 32, 35)( 33, 34)( 37, 40)( 38, 39)( 42, 45)( 43, 44)( 46, 61)( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 51, 66)( 52, 70)( 53, 69)( 54, 68)( 55, 67)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 77, 80)( 78, 79)( 82, 85)( 83, 84)( 87, 90)( 88, 89)( 91,151)( 92,155)( 93,154)( 94,153)( 95,152)( 96,156)( 97,160)( 98,159)( 99,158)(100,157)(101,161)(102,165)(103,164)(104,163)(105,162)(106,136)(107,140)(108,139)(109,138)(110,137)(111,141)(112,145)(113,144)(114,143)(115,142)(116,146)(117,150)(118,149)(119,148)(120,147)(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); s3 := Sym(180)!( 1, 92)( 2, 91)( 3, 95)( 4, 94)( 5, 93)( 6, 97)( 7, 96)( 8,100)( 9, 99)( 10, 98)( 11,102)( 12,101)( 13,105)( 14,104)( 15,103)( 16,107)( 17,106)( 18,110)( 19,109)( 20,108)( 21,112)( 22,111)( 23,115)( 24,114)( 25,113)( 26,117)( 27,116)( 28,120)( 29,119)( 30,118)( 31,122)( 32,121)( 33,125)( 34,124)( 35,123)( 36,127)( 37,126)( 38,130)( 39,129)( 40,128)( 41,132)( 42,131)( 43,135)( 44,134)( 45,133)( 46,137)( 47,136)( 48,140)( 49,139)( 50,138)( 51,142)( 52,141)( 53,145)( 54,144)( 55,143)( 56,147)( 57,146)( 58,150)( 59,149)( 60,148)( 61,152)( 62,151)( 63,155)( 64,154)( 65,153)( 66,157)( 67,156)( 68,160)( 69,159)( 70,158)( 71,162)( 72,161)( 73,165)( 74,164)( 75,163)( 76,167)( 77,166)( 78,170)( 79,169)( 80,168)( 81,172)( 82,171)( 83,175)( 84,174)( 85,173)( 86,177)( 87,176)( 88,180)( 89,179)( 90,178); 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, s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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.