Overview
- Group
- SmallGroup(1728,46115)
- Rank
- 5
- Schläfli Type
- {2,6,18,4}
- Vertices, edges, …
- 2, 6, 54, 36, 4
- Order of s0s1s2s3s4
- 18
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
6-fold
9-fold
18-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 25, 37)( 26, 38)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 69)( 58, 70)( 59, 71)( 60, 72)( 61, 73)( 62, 74)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,103)( 92,104)( 93,105)( 94,106)( 95,107)( 96,108)( 97,109)( 98,110)(123,135)(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)(131,143)(132,144)(133,145)(134,146)(159,171)(160,172)(161,173)(162,174)(163,175)(164,176)(165,177)(166,178)(167,179)(168,180)(169,181)(170,182)(195,207)(196,208)(197,209)(198,210)(199,211)(200,212)(201,213)(202,214)(203,215)(204,216)(205,217)(206,218);; s2 := ( 3, 15)( 4, 17)( 5, 16)( 6, 18)( 7, 23)( 8, 25)( 9, 24)( 10, 26)( 11, 19)( 12, 21)( 13, 20)( 14, 22)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)( 39, 91)( 40, 93)( 41, 92)( 42, 94)( 43, 87)( 44, 89)( 45, 88)( 46, 90)( 47, 95)( 48, 97)( 49, 96)( 50, 98)( 51, 79)( 52, 81)( 53, 80)( 54, 82)( 55, 75)( 56, 77)( 57, 76)( 58, 78)( 59, 83)( 60, 85)( 61, 84)( 62, 86)( 63,103)( 64,105)( 65,104)( 66,106)( 67, 99)( 68,101)( 69,100)( 70,102)( 71,107)( 72,109)( 73,108)( 74,110)(111,123)(112,125)(113,124)(114,126)(115,131)(116,133)(117,132)(118,134)(119,127)(120,129)(121,128)(122,130)(136,137)(139,143)(140,145)(141,144)(142,146)(147,199)(148,201)(149,200)(150,202)(151,195)(152,197)(153,196)(154,198)(155,203)(156,205)(157,204)(158,206)(159,187)(160,189)(161,188)(162,190)(163,183)(164,185)(165,184)(166,186)(167,191)(168,193)(169,192)(170,194)(171,211)(172,213)(173,212)(174,214)(175,207)(176,209)(177,208)(178,210)(179,215)(180,217)(181,216)(182,218);; s3 := ( 3,147)( 4,148)( 5,150)( 6,149)( 7,155)( 8,156)( 9,158)( 10,157)( 11,151)( 12,152)( 13,154)( 14,153)( 15,159)( 16,160)( 17,162)( 18,161)( 19,167)( 20,168)( 21,170)( 22,169)( 23,163)( 24,164)( 25,166)( 26,165)( 27,171)( 28,172)( 29,174)( 30,173)( 31,179)( 32,180)( 33,182)( 34,181)( 35,175)( 36,176)( 37,178)( 38,177)( 39,111)( 40,112)( 41,114)( 42,113)( 43,119)( 44,120)( 45,122)( 46,121)( 47,115)( 48,116)( 49,118)( 50,117)( 51,123)( 52,124)( 53,126)( 54,125)( 55,131)( 56,132)( 57,134)( 58,133)( 59,127)( 60,128)( 61,130)( 62,129)( 63,135)( 64,136)( 65,138)( 66,137)( 67,143)( 68,144)( 69,146)( 70,145)( 71,139)( 72,140)( 73,142)( 74,141)( 75,187)( 76,188)( 77,190)( 78,189)( 79,183)( 80,184)( 81,186)( 82,185)( 83,191)( 84,192)( 85,194)( 86,193)( 87,199)( 88,200)( 89,202)( 90,201)( 91,195)( 92,196)( 93,198)( 94,197)( 95,203)( 96,204)( 97,206)( 98,205)( 99,211)(100,212)(101,214)(102,213)(103,207)(104,208)(105,210)(106,209)(107,215)(108,216)(109,218)(110,217);; s4 := ( 3, 6)( 4, 5)( 7, 10)( 8, 9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)(128,129)(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)(144,145)(147,150)(148,149)(151,154)(152,153)(155,158)(156,157)(159,162)(160,161)(163,166)(164,165)(167,170)(168,169)(171,174)(172,173)(175,178)(176,177)(179,182)(180,181)(183,186)(184,185)(187,190)(188,189)(191,194)(192,193)(195,198)(196,197)(199,202)(200,201)(203,206)(204,205)(207,210)(208,209)(211,214)(212,213)(215,218)(216,217);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s4*s3*s4*s3*s2*s3, 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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(218)!(1,2); s1 := Sym(218)!( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 31)( 20, 32)( 21, 33)( 22, 34)( 23, 35)( 24, 36)( 25, 37)( 26, 38)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 67)( 56, 68)( 57, 69)( 58, 70)( 59, 71)( 60, 72)( 61, 73)( 62, 74)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,103)( 92,104)( 93,105)( 94,106)( 95,107)( 96,108)( 97,109)( 98,110)(123,135)(124,136)(125,137)(126,138)(127,139)(128,140)(129,141)(130,142)(131,143)(132,144)(133,145)(134,146)(159,171)(160,172)(161,173)(162,174)(163,175)(164,176)(165,177)(166,178)(167,179)(168,180)(169,181)(170,182)(195,207)(196,208)(197,209)(198,210)(199,211)(200,212)(201,213)(202,214)(203,215)(204,216)(205,217)(206,218); s2 := Sym(218)!( 3, 15)( 4, 17)( 5, 16)( 6, 18)( 7, 23)( 8, 25)( 9, 24)( 10, 26)( 11, 19)( 12, 21)( 13, 20)( 14, 22)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)( 39, 91)( 40, 93)( 41, 92)( 42, 94)( 43, 87)( 44, 89)( 45, 88)( 46, 90)( 47, 95)( 48, 97)( 49, 96)( 50, 98)( 51, 79)( 52, 81)( 53, 80)( 54, 82)( 55, 75)( 56, 77)( 57, 76)( 58, 78)( 59, 83)( 60, 85)( 61, 84)( 62, 86)( 63,103)( 64,105)( 65,104)( 66,106)( 67, 99)( 68,101)( 69,100)( 70,102)( 71,107)( 72,109)( 73,108)( 74,110)(111,123)(112,125)(113,124)(114,126)(115,131)(116,133)(117,132)(118,134)(119,127)(120,129)(121,128)(122,130)(136,137)(139,143)(140,145)(141,144)(142,146)(147,199)(148,201)(149,200)(150,202)(151,195)(152,197)(153,196)(154,198)(155,203)(156,205)(157,204)(158,206)(159,187)(160,189)(161,188)(162,190)(163,183)(164,185)(165,184)(166,186)(167,191)(168,193)(169,192)(170,194)(171,211)(172,213)(173,212)(174,214)(175,207)(176,209)(177,208)(178,210)(179,215)(180,217)(181,216)(182,218); s3 := Sym(218)!( 3,147)( 4,148)( 5,150)( 6,149)( 7,155)( 8,156)( 9,158)( 10,157)( 11,151)( 12,152)( 13,154)( 14,153)( 15,159)( 16,160)( 17,162)( 18,161)( 19,167)( 20,168)( 21,170)( 22,169)( 23,163)( 24,164)( 25,166)( 26,165)( 27,171)( 28,172)( 29,174)( 30,173)( 31,179)( 32,180)( 33,182)( 34,181)( 35,175)( 36,176)( 37,178)( 38,177)( 39,111)( 40,112)( 41,114)( 42,113)( 43,119)( 44,120)( 45,122)( 46,121)( 47,115)( 48,116)( 49,118)( 50,117)( 51,123)( 52,124)( 53,126)( 54,125)( 55,131)( 56,132)( 57,134)( 58,133)( 59,127)( 60,128)( 61,130)( 62,129)( 63,135)( 64,136)( 65,138)( 66,137)( 67,143)( 68,144)( 69,146)( 70,145)( 71,139)( 72,140)( 73,142)( 74,141)( 75,187)( 76,188)( 77,190)( 78,189)( 79,183)( 80,184)( 81,186)( 82,185)( 83,191)( 84,192)( 85,194)( 86,193)( 87,199)( 88,200)( 89,202)( 90,201)( 91,195)( 92,196)( 93,198)( 94,197)( 95,203)( 96,204)( 97,206)( 98,205)( 99,211)(100,212)(101,214)(102,213)(103,207)(104,208)(105,210)(106,209)(107,215)(108,216)(109,218)(110,217); s4 := Sym(218)!( 3, 6)( 4, 5)( 7, 10)( 8, 9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)(128,129)(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)(144,145)(147,150)(148,149)(151,154)(152,153)(155,158)(156,157)(159,162)(160,161)(163,166)(164,165)(167,170)(168,169)(171,174)(172,173)(175,178)(176,177)(179,182)(180,181)(183,186)(184,185)(187,190)(188,189)(191,194)(192,193)(195,198)(196,197)(199,202)(200,201)(203,206)(204,205)(207,210)(208,209)(211,214)(212,213)(215,218)(216,217); poly := sub<Sym(218)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3, 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 >;