Overview
- Group
- SmallGroup(1440,5360)
- Rank
- 4
- Schläfli Type
- {30,6,4}
- Vertices, edges, …
- 30, 90, 12, 4
- 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 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 16, 31)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 36)( 22, 40)( 23, 39)( 24, 38)( 25, 37)( 26, 41)( 27, 45)( 28, 44)( 29, 43)( 30, 42)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)( 61, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 81)( 67, 85)( 68, 84)( 69, 83)( 70, 82)( 71, 86)( 72, 90)( 73, 89)( 74, 88)( 75, 87)( 92, 95)( 93, 94)( 97,100)( 98, 99)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,126)(112,130)(113,129)(114,128)(115,127)(116,131)(117,135)(118,134)(119,133)(120,132)(137,140)(138,139)(142,145)(143,144)(147,150)(148,149)(151,166)(152,170)(153,169)(154,168)(155,167)(156,171)(157,175)(158,174)(159,173)(160,172)(161,176)(162,180)(163,179)(164,178)(165,177);; s1 := ( 1, 17)( 2, 16)( 3, 20)( 4, 19)( 5, 18)( 6, 27)( 7, 26)( 8, 30)( 9, 29)( 10, 28)( 11, 22)( 12, 21)( 13, 25)( 14, 24)( 15, 23)( 31, 32)( 33, 35)( 36, 42)( 37, 41)( 38, 45)( 39, 44)( 40, 43)( 46, 62)( 47, 61)( 48, 65)( 49, 64)( 50, 63)( 51, 72)( 52, 71)( 53, 75)( 54, 74)( 55, 73)( 56, 67)( 57, 66)( 58, 70)( 59, 69)( 60, 68)( 76, 77)( 78, 80)( 81, 87)( 82, 86)( 83, 90)( 84, 89)( 85, 88)( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)( 96,117)( 97,116)( 98,120)( 99,119)(100,118)(101,112)(102,111)(103,115)(104,114)(105,113)(121,122)(123,125)(126,132)(127,131)(128,135)(129,134)(130,133)(136,152)(137,151)(138,155)(139,154)(140,153)(141,162)(142,161)(143,165)(144,164)(145,163)(146,157)(147,156)(148,160)(149,159)(150,158)(166,167)(168,170)(171,177)(172,176)(173,180)(174,179)(175,178);; 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)( 91,141)( 92,142)( 93,143)( 94,144)( 95,145)( 96,136)( 97,137)( 98,138)( 99,139)(100,140)(101,146)(102,147)(103,148)(104,149)(105,150)(106,171)(107,172)(108,173)(109,174)(110,175)(111,166)(112,167)(113,168)(114,169)(115,170)(116,176)(117,177)(118,178)(119,179)(120,180)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)(128,153)(129,154)(130,155)(131,161)(132,162)(133,163)(134,164)(135,165);; s3 := ( 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);; 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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*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)( 16, 31)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 36)( 22, 40)( 23, 39)( 24, 38)( 25, 37)( 26, 41)( 27, 45)( 28, 44)( 29, 43)( 30, 42)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)( 61, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 81)( 67, 85)( 68, 84)( 69, 83)( 70, 82)( 71, 86)( 72, 90)( 73, 89)( 74, 88)( 75, 87)( 92, 95)( 93, 94)( 97,100)( 98, 99)(102,105)(103,104)(106,121)(107,125)(108,124)(109,123)(110,122)(111,126)(112,130)(113,129)(114,128)(115,127)(116,131)(117,135)(118,134)(119,133)(120,132)(137,140)(138,139)(142,145)(143,144)(147,150)(148,149)(151,166)(152,170)(153,169)(154,168)(155,167)(156,171)(157,175)(158,174)(159,173)(160,172)(161,176)(162,180)(163,179)(164,178)(165,177); s1 := Sym(180)!( 1, 17)( 2, 16)( 3, 20)( 4, 19)( 5, 18)( 6, 27)( 7, 26)( 8, 30)( 9, 29)( 10, 28)( 11, 22)( 12, 21)( 13, 25)( 14, 24)( 15, 23)( 31, 32)( 33, 35)( 36, 42)( 37, 41)( 38, 45)( 39, 44)( 40, 43)( 46, 62)( 47, 61)( 48, 65)( 49, 64)( 50, 63)( 51, 72)( 52, 71)( 53, 75)( 54, 74)( 55, 73)( 56, 67)( 57, 66)( 58, 70)( 59, 69)( 60, 68)( 76, 77)( 78, 80)( 81, 87)( 82, 86)( 83, 90)( 84, 89)( 85, 88)( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)( 96,117)( 97,116)( 98,120)( 99,119)(100,118)(101,112)(102,111)(103,115)(104,114)(105,113)(121,122)(123,125)(126,132)(127,131)(128,135)(129,134)(130,133)(136,152)(137,151)(138,155)(139,154)(140,153)(141,162)(142,161)(143,165)(144,164)(145,163)(146,157)(147,156)(148,160)(149,159)(150,158)(166,167)(168,170)(171,177)(172,176)(173,180)(174,179)(175,178); 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)( 91,141)( 92,142)( 93,143)( 94,144)( 95,145)( 96,136)( 97,137)( 98,138)( 99,139)(100,140)(101,146)(102,147)(103,148)(104,149)(105,150)(106,171)(107,172)(108,173)(109,174)(110,175)(111,166)(112,167)(113,168)(114,169)(115,170)(116,176)(117,177)(118,178)(119,179)(120,180)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)(128,153)(129,154)(130,155)(131,161)(132,162)(133,163)(134,164)(135,165); s3 := 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); 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, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 >;
References
None.
to this polytope.