Overview
- Group
- SmallGroup(1440,5358)
- Rank
- 4
- Schläfli Type
- {4,30,6}
- Vertices, edges, …
- 4, 60, 90, 6
- Order of s0s1s2s3
- 60
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
5-fold
6-fold
9-fold
10-fold
15-fold
18-fold
20-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 := ( 1, 91)( 2, 92)( 3, 93)( 4, 94)( 5, 95)( 6, 96)( 7, 97)( 8, 98)( 9, 99)( 10,100)( 11,101)( 12,102)( 13,103)( 14,104)( 15,105)( 16,106)( 17,107)( 18,108)( 19,109)( 20,110)( 21,111)( 22,112)( 23,113)( 24,114)( 25,115)( 26,116)( 27,117)( 28,118)( 29,119)( 30,120)( 31,121)( 32,122)( 33,123)( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,129)( 40,130)( 41,131)( 42,132)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)( 50,140)( 51,141)( 52,142)( 53,143)( 54,144)( 55,145)( 56,146)( 57,147)( 58,148)( 59,149)( 60,150)( 61,151)( 62,152)( 63,153)( 64,154)( 65,155)( 66,156)( 67,157)( 68,158)( 69,159)( 70,160)( 71,161)( 72,162)( 73,163)( 74,164)( 75,165)( 76,166)( 77,167)( 78,168)( 79,169)( 80,170)( 81,171)( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,177)( 88,178)( 89,179)( 90,180);; s1 := ( 2, 5)( 3, 4)( 6, 11)( 7, 15)( 8, 14)( 9, 13)( 10, 12)( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,136)( 92,140)( 93,139)( 94,138)( 95,137)( 96,146)( 97,150)( 98,149)( 99,148)(100,147)(101,141)(102,145)(103,144)(104,143)(105,142)(106,151)(107,155)(108,154)(109,153)(110,152)(111,161)(112,165)(113,164)(114,163)(115,162)(116,156)(117,160)(118,159)(119,158)(120,157)(121,166)(122,170)(123,169)(124,168)(125,167)(126,176)(127,180)(128,179)(129,178)(130,177)(131,171)(132,175)(133,174)(134,173)(135,172);; s2 := ( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)( 16, 37)( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)( 24, 34)( 25, 33)( 26, 42)( 27, 41)( 28, 45)( 29, 44)( 30, 43)( 46, 52)( 47, 51)( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 82)( 62, 81)( 63, 85)( 64, 84)( 65, 83)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 71, 87)( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)(101,102)(103,105)(106,127)(107,126)(108,130)(109,129)(110,128)(111,122)(112,121)(113,125)(114,124)(115,123)(116,132)(117,131)(118,135)(119,134)(120,133)(136,142)(137,141)(138,145)(139,144)(140,143)(146,147)(148,150)(151,172)(152,171)(153,175)(154,174)(155,173)(156,167)(157,166)(158,170)(159,169)(160,168)(161,177)(162,176)(163,180)(164,179)(165,178);; s3 := ( 1, 16)( 2, 17)( 3, 18)( 4, 19)( 5, 20)( 6, 26)( 7, 27)( 8, 28)( 9, 29)( 10, 30)( 11, 21)( 12, 22)( 13, 23)( 14, 24)( 15, 25)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 46, 61)( 47, 62)( 48, 63)( 49, 64)( 50, 65)( 51, 71)( 52, 72)( 53, 73)( 54, 74)( 55, 75)( 56, 66)( 57, 67)( 58, 68)( 59, 69)( 60, 70)( 81, 86)( 82, 87)( 83, 88)( 84, 89)( 85, 90)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,116)( 97,117)( 98,118)( 99,119)(100,120)(101,111)(102,112)(103,113)(104,114)(105,115)(126,131)(127,132)(128,133)(129,134)(130,135)(136,151)(137,152)(138,153)(139,154)(140,155)(141,161)(142,162)(143,163)(144,164)(145,165)(146,156)(147,157)(148,158)(149,159)(150,160)(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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(180)!( 1, 91)( 2, 92)( 3, 93)( 4, 94)( 5, 95)( 6, 96)( 7, 97)( 8, 98)( 9, 99)( 10,100)( 11,101)( 12,102)( 13,103)( 14,104)( 15,105)( 16,106)( 17,107)( 18,108)( 19,109)( 20,110)( 21,111)( 22,112)( 23,113)( 24,114)( 25,115)( 26,116)( 27,117)( 28,118)( 29,119)( 30,120)( 31,121)( 32,122)( 33,123)( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,129)( 40,130)( 41,131)( 42,132)( 43,133)( 44,134)( 45,135)( 46,136)( 47,137)( 48,138)( 49,139)( 50,140)( 51,141)( 52,142)( 53,143)( 54,144)( 55,145)( 56,146)( 57,147)( 58,148)( 59,149)( 60,150)( 61,151)( 62,152)( 63,153)( 64,154)( 65,155)( 66,156)( 67,157)( 68,158)( 69,159)( 70,160)( 71,161)( 72,162)( 73,163)( 74,164)( 75,165)( 76,166)( 77,167)( 78,168)( 79,169)( 80,170)( 81,171)( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,177)( 88,178)( 89,179)( 90,180); s1 := Sym(180)!( 2, 5)( 3, 4)( 6, 11)( 7, 15)( 8, 14)( 9, 13)( 10, 12)( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 91,136)( 92,140)( 93,139)( 94,138)( 95,137)( 96,146)( 97,150)( 98,149)( 99,148)(100,147)(101,141)(102,145)(103,144)(104,143)(105,142)(106,151)(107,155)(108,154)(109,153)(110,152)(111,161)(112,165)(113,164)(114,163)(115,162)(116,156)(117,160)(118,159)(119,158)(120,157)(121,166)(122,170)(123,169)(124,168)(125,167)(126,176)(127,180)(128,179)(129,178)(130,177)(131,171)(132,175)(133,174)(134,173)(135,172); s2 := Sym(180)!( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)( 16, 37)( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)( 24, 34)( 25, 33)( 26, 42)( 27, 41)( 28, 45)( 29, 44)( 30, 43)( 46, 52)( 47, 51)( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 82)( 62, 81)( 63, 85)( 64, 84)( 65, 83)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 71, 87)( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)(101,102)(103,105)(106,127)(107,126)(108,130)(109,129)(110,128)(111,122)(112,121)(113,125)(114,124)(115,123)(116,132)(117,131)(118,135)(119,134)(120,133)(136,142)(137,141)(138,145)(139,144)(140,143)(146,147)(148,150)(151,172)(152,171)(153,175)(154,174)(155,173)(156,167)(157,166)(158,170)(159,169)(160,168)(161,177)(162,176)(163,180)(164,179)(165,178); s3 := Sym(180)!( 1, 16)( 2, 17)( 3, 18)( 4, 19)( 5, 20)( 6, 26)( 7, 27)( 8, 28)( 9, 29)( 10, 30)( 11, 21)( 12, 22)( 13, 23)( 14, 24)( 15, 25)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 46, 61)( 47, 62)( 48, 63)( 49, 64)( 50, 65)( 51, 71)( 52, 72)( 53, 73)( 54, 74)( 55, 75)( 56, 66)( 57, 67)( 58, 68)( 59, 69)( 60, 70)( 81, 86)( 82, 87)( 83, 88)( 84, 89)( 85, 90)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,116)( 97,117)( 98,118)( 99,119)(100,120)(101,111)(102,112)(103,113)(104,114)(105,115)(126,131)(127,132)(128,133)(129,134)(130,135)(136,151)(137,152)(138,153)(139,154)(140,155)(141,161)(142,162)(143,163)(144,164)(145,165)(146,156)(147,157)(148,158)(149,159)(150,160)(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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >;
References
None.
to this polytope.