Overview
- Group
- SmallGroup(1440,1593)
- Rank
- 4
- Schläfli Type
- {10,18,4}
- Vertices, edges, …
- 10, 90, 36, 4
- Order of s0s1s2s3
- 180
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{10,18|2},{18,4|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
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 := ( 4, 13)( 5, 14)( 6, 15)( 7, 10)( 8, 11)( 9, 12)( 19, 28)( 20, 29)( 21, 30)( 22, 25)( 23, 26)( 24, 27)( 34, 43)( 35, 44)( 36, 45)( 37, 40)( 38, 41)( 39, 42)( 49, 58)( 50, 59)( 51, 60)( 52, 55)( 53, 56)( 54, 57)( 64, 73)( 65, 74)( 66, 75)( 67, 70)( 68, 71)( 69, 72)( 79, 88)( 80, 89)( 81, 90)( 82, 85)( 83, 86)( 84, 87)( 94,103)( 95,104)( 96,105)( 97,100)( 98,101)( 99,102)(109,118)(110,119)(111,120)(112,115)(113,116)(114,117)(124,133)(125,134)(126,135)(127,130)(128,131)(129,132)(139,148)(140,149)(141,150)(142,145)(143,146)(144,147)(154,163)(155,164)(156,165)(157,160)(158,161)(159,162)(169,178)(170,179)(171,180)(172,175)(173,176)(174,177);; s1 := ( 1, 4)( 2, 6)( 3, 5)( 7, 13)( 8, 15)( 9, 14)( 11, 12)( 16, 36)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 31)( 22, 45)( 23, 44)( 24, 43)( 25, 42)( 26, 41)( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 46, 49)( 47, 51)( 48, 50)( 52, 58)( 53, 60)( 54, 59)( 56, 57)( 61, 81)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 76)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 91, 94)( 92, 96)( 93, 95)( 97,103)( 98,105)( 99,104)(101,102)(106,126)(107,125)(108,124)(109,123)(110,122)(111,121)(112,135)(113,134)(114,133)(115,132)(116,131)(117,130)(118,129)(119,128)(120,127)(136,139)(137,141)(138,140)(142,148)(143,150)(144,149)(146,147)(151,171)(152,170)(153,169)(154,168)(155,167)(156,166)(157,180)(158,179)(159,178)(160,177)(161,176)(162,175)(163,174)(164,173)(165,172);; s2 := ( 1, 16)( 2, 18)( 3, 17)( 4, 19)( 5, 21)( 6, 20)( 7, 22)( 8, 24)( 9, 23)( 10, 25)( 11, 27)( 12, 26)( 13, 28)( 14, 30)( 15, 29)( 31, 33)( 34, 36)( 37, 39)( 40, 42)( 43, 45)( 46, 61)( 47, 63)( 48, 62)( 49, 64)( 50, 66)( 51, 65)( 52, 67)( 53, 69)( 54, 68)( 55, 70)( 56, 72)( 57, 71)( 58, 73)( 59, 75)( 60, 74)( 76, 78)( 79, 81)( 82, 84)( 85, 87)( 88, 90)( 91,151)( 92,153)( 93,152)( 94,154)( 95,156)( 96,155)( 97,157)( 98,159)( 99,158)(100,160)(101,162)(102,161)(103,163)(104,165)(105,164)(106,136)(107,138)(108,137)(109,139)(110,141)(111,140)(112,142)(113,144)(114,143)(115,145)(116,147)(117,146)(118,148)(119,150)(120,149)(121,168)(122,167)(123,166)(124,171)(125,170)(126,169)(127,174)(128,173)(129,172)(130,177)(131,176)(132,175)(133,180)(134,179)(135,178);; 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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(180)!( 4, 13)( 5, 14)( 6, 15)( 7, 10)( 8, 11)( 9, 12)( 19, 28)( 20, 29)( 21, 30)( 22, 25)( 23, 26)( 24, 27)( 34, 43)( 35, 44)( 36, 45)( 37, 40)( 38, 41)( 39, 42)( 49, 58)( 50, 59)( 51, 60)( 52, 55)( 53, 56)( 54, 57)( 64, 73)( 65, 74)( 66, 75)( 67, 70)( 68, 71)( 69, 72)( 79, 88)( 80, 89)( 81, 90)( 82, 85)( 83, 86)( 84, 87)( 94,103)( 95,104)( 96,105)( 97,100)( 98,101)( 99,102)(109,118)(110,119)(111,120)(112,115)(113,116)(114,117)(124,133)(125,134)(126,135)(127,130)(128,131)(129,132)(139,148)(140,149)(141,150)(142,145)(143,146)(144,147)(154,163)(155,164)(156,165)(157,160)(158,161)(159,162)(169,178)(170,179)(171,180)(172,175)(173,176)(174,177); s1 := Sym(180)!( 1, 4)( 2, 6)( 3, 5)( 7, 13)( 8, 15)( 9, 14)( 11, 12)( 16, 36)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 31)( 22, 45)( 23, 44)( 24, 43)( 25, 42)( 26, 41)( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 46, 49)( 47, 51)( 48, 50)( 52, 58)( 53, 60)( 54, 59)( 56, 57)( 61, 81)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 76)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 91, 94)( 92, 96)( 93, 95)( 97,103)( 98,105)( 99,104)(101,102)(106,126)(107,125)(108,124)(109,123)(110,122)(111,121)(112,135)(113,134)(114,133)(115,132)(116,131)(117,130)(118,129)(119,128)(120,127)(136,139)(137,141)(138,140)(142,148)(143,150)(144,149)(146,147)(151,171)(152,170)(153,169)(154,168)(155,167)(156,166)(157,180)(158,179)(159,178)(160,177)(161,176)(162,175)(163,174)(164,173)(165,172); s2 := Sym(180)!( 1, 16)( 2, 18)( 3, 17)( 4, 19)( 5, 21)( 6, 20)( 7, 22)( 8, 24)( 9, 23)( 10, 25)( 11, 27)( 12, 26)( 13, 28)( 14, 30)( 15, 29)( 31, 33)( 34, 36)( 37, 39)( 40, 42)( 43, 45)( 46, 61)( 47, 63)( 48, 62)( 49, 64)( 50, 66)( 51, 65)( 52, 67)( 53, 69)( 54, 68)( 55, 70)( 56, 72)( 57, 71)( 58, 73)( 59, 75)( 60, 74)( 76, 78)( 79, 81)( 82, 84)( 85, 87)( 88, 90)( 91,151)( 92,153)( 93,152)( 94,154)( 95,156)( 96,155)( 97,157)( 98,159)( 99,158)(100,160)(101,162)(102,161)(103,163)(104,165)(105,164)(106,136)(107,138)(108,137)(109,139)(110,141)(111,140)(112,142)(113,144)(114,143)(115,145)(116,147)(117,146)(118,148)(119,150)(120,149)(121,168)(122,167)(123,166)(124,171)(125,170)(126,169)(127,174)(128,173)(129,172)(130,177)(131,176)(132,175)(133,180)(134,179)(135,178); 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, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.