Overview
- Group
- SmallGroup(1440,5284)
- Rank
- 4
- Schläfli Type
- {20,6,6}
- Vertices, edges, …
- 20, 60, 18, 6
- Order of s0s1s2s3
- 60
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{20,6|2},{6,6|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 := ( 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)( 16,107)( 17,106)( 18,110)( 19,109)( 20,108)( 21,117)( 22,116)( 23,120)( 24,119)( 25,118)( 26,112)( 27,111)( 28,115)( 29,114)( 30,113)( 31,122)( 32,121)( 33,125)( 34,124)( 35,123)( 36,132)( 37,131)( 38,135)( 39,134)( 40,133)( 41,127)( 42,126)( 43,130)( 44,129)( 45,128)( 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)( 61,152)( 62,151)( 63,155)( 64,154)( 65,153)( 66,162)( 67,161)( 68,165)( 69,164)( 70,163)( 71,157)( 72,156)( 73,160)( 74,159)( 75,158)( 76,167)( 77,166)( 78,170)( 79,169)( 80,168)( 81,177)( 82,176)( 83,180)( 84,179)( 85,178)( 86,172)( 87,171)( 88,175)( 89,174)( 90,173);; s2 := ( 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);; s3 := ( 1, 16)( 2, 17)( 3, 18)( 4, 19)( 5, 20)( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 28)( 14, 29)( 15, 30)( 46, 61)( 47, 62)( 48, 63)( 49, 64)( 50, 65)( 51, 66)( 52, 67)( 53, 68)( 54, 69)( 55, 70)( 56, 71)( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(136,151)(137,152)(138,153)(139,154)(140,155)(141,156)(142,157)(143,158)(144,159)(145,160)(146,161)(147,162)(148,163)(149,164)(150,165);; 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)( 16,107)( 17,106)( 18,110)( 19,109)( 20,108)( 21,117)( 22,116)( 23,120)( 24,119)( 25,118)( 26,112)( 27,111)( 28,115)( 29,114)( 30,113)( 31,122)( 32,121)( 33,125)( 34,124)( 35,123)( 36,132)( 37,131)( 38,135)( 39,134)( 40,133)( 41,127)( 42,126)( 43,130)( 44,129)( 45,128)( 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)( 61,152)( 62,151)( 63,155)( 64,154)( 65,153)( 66,162)( 67,161)( 68,165)( 69,164)( 70,163)( 71,157)( 72,156)( 73,160)( 74,159)( 75,158)( 76,167)( 77,166)( 78,170)( 79,169)( 80,168)( 81,177)( 82,176)( 83,180)( 84,179)( 85,178)( 86,172)( 87,171)( 88,175)( 89,174)( 90,173); s2 := 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); s3 := Sym(180)!( 1, 16)( 2, 17)( 3, 18)( 4, 19)( 5, 20)( 6, 21)( 7, 22)( 8, 23)( 9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 28)( 14, 29)( 15, 30)( 46, 61)( 47, 62)( 48, 63)( 49, 64)( 50, 65)( 51, 66)( 52, 67)( 53, 68)( 54, 69)( 55, 70)( 56, 71)( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(136,151)(137,152)(138,153)(139,154)(140,155)(141,156)(142,157)(143,158)(144,159)(145,160)(146,161)(147,162)(148,163)(149,164)(150,165); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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.