Overview
- Group
- SmallGroup(1728,46116)
- Rank
- 5
- Schläfli Type
- {2,4,6,6}
- Vertices, edges, …
- 2, 4, 36, 54, 18
- Order of s0s1s2s3s4
- 6
- 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
2-fold
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 := ( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)(128,130)(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)(144,146)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)(160,162)(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)(176,178)(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)(192,194)(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)(208,210)(211,213)(212,214)(215,217)(216,218);; s2 := ( 4, 5)( 8, 9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)( 39, 75)( 40, 77)( 41, 76)( 42, 78)( 43, 79)( 44, 81)( 45, 80)( 46, 82)( 47, 83)( 48, 85)( 49, 84)( 50, 86)( 51, 99)( 52,101)( 53,100)( 54,102)( 55,103)( 56,105)( 57,104)( 58,106)( 59,107)( 60,109)( 61,108)( 62,110)( 63, 87)( 64, 89)( 65, 88)( 66, 90)( 67, 91)( 68, 93)( 69, 92)( 70, 94)( 71, 95)( 72, 97)( 73, 96)( 74, 98)(112,113)(116,117)(120,121)(123,135)(124,137)(125,136)(126,138)(127,139)(128,141)(129,140)(130,142)(131,143)(132,145)(133,144)(134,146)(147,183)(148,185)(149,184)(150,186)(151,187)(152,189)(153,188)(154,190)(155,191)(156,193)(157,192)(158,194)(159,207)(160,209)(161,208)(162,210)(163,211)(164,213)(165,212)(166,214)(167,215)(168,217)(169,216)(170,218)(171,195)(172,197)(173,196)(174,198)(175,199)(176,201)(177,200)(178,202)(179,203)(180,205)(181,204)(182,206);; s3 := ( 3,199)( 4,202)( 5,201)( 6,200)( 7,203)( 8,206)( 9,205)( 10,204)( 11,195)( 12,198)( 13,197)( 14,196)( 15,191)( 16,194)( 17,193)( 18,192)( 19,183)( 20,186)( 21,185)( 22,184)( 23,187)( 24,190)( 25,189)( 26,188)( 27,207)( 28,210)( 29,209)( 30,208)( 31,211)( 32,214)( 33,213)( 34,212)( 35,215)( 36,218)( 37,217)( 38,216)( 39,163)( 40,166)( 41,165)( 42,164)( 43,167)( 44,170)( 45,169)( 46,168)( 47,159)( 48,162)( 49,161)( 50,160)( 51,155)( 52,158)( 53,157)( 54,156)( 55,147)( 56,150)( 57,149)( 58,148)( 59,151)( 60,154)( 61,153)( 62,152)( 63,171)( 64,174)( 65,173)( 66,172)( 67,175)( 68,178)( 69,177)( 70,176)( 71,179)( 72,182)( 73,181)( 74,180)( 75,127)( 76,130)( 77,129)( 78,128)( 79,131)( 80,134)( 81,133)( 82,132)( 83,123)( 84,126)( 85,125)( 86,124)( 87,119)( 88,122)( 89,121)( 90,120)( 91,111)( 92,114)( 93,113)( 94,112)( 95,115)( 96,118)( 97,117)( 98,116)( 99,135)(100,138)(101,137)(102,136)(103,139)(104,142)(105,141)(106,140)(107,143)(108,146)(109,145)(110,144);; s4 := ( 7, 11)( 8, 12)( 9, 13)( 10, 14)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 31)( 24, 32)( 25, 33)( 26, 34)( 43, 47)( 44, 48)( 45, 49)( 46, 50)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 71)( 56, 72)( 57, 73)( 58, 74)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 79, 83)( 80, 84)( 81, 85)( 82, 86)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,107)( 92,108)( 93,109)( 94,110)( 95,103)( 96,104)( 97,105)( 98,106)(115,119)(116,120)(117,121)(118,122)(123,135)(124,136)(125,137)(126,138)(127,143)(128,144)(129,145)(130,146)(131,139)(132,140)(133,141)(134,142)(151,155)(152,156)(153,157)(154,158)(159,171)(160,172)(161,173)(162,174)(163,179)(164,180)(165,181)(166,182)(167,175)(168,176)(169,177)(170,178)(187,191)(188,192)(189,193)(190,194)(195,207)(196,208)(197,209)(198,210)(199,215)(200,216)(201,217)(202,218)(203,211)(204,212)(205,213)(206,214);; 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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(218)!(1,2); s1 := Sym(218)!( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)(128,130)(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)(144,146)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)(160,162)(163,165)(164,166)(167,169)(168,170)(171,173)(172,174)(175,177)(176,178)(179,181)(180,182)(183,185)(184,186)(187,189)(188,190)(191,193)(192,194)(195,197)(196,198)(199,201)(200,202)(203,205)(204,206)(207,209)(208,210)(211,213)(212,214)(215,217)(216,218); s2 := Sym(218)!( 4, 5)( 8, 9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)( 39, 75)( 40, 77)( 41, 76)( 42, 78)( 43, 79)( 44, 81)( 45, 80)( 46, 82)( 47, 83)( 48, 85)( 49, 84)( 50, 86)( 51, 99)( 52,101)( 53,100)( 54,102)( 55,103)( 56,105)( 57,104)( 58,106)( 59,107)( 60,109)( 61,108)( 62,110)( 63, 87)( 64, 89)( 65, 88)( 66, 90)( 67, 91)( 68, 93)( 69, 92)( 70, 94)( 71, 95)( 72, 97)( 73, 96)( 74, 98)(112,113)(116,117)(120,121)(123,135)(124,137)(125,136)(126,138)(127,139)(128,141)(129,140)(130,142)(131,143)(132,145)(133,144)(134,146)(147,183)(148,185)(149,184)(150,186)(151,187)(152,189)(153,188)(154,190)(155,191)(156,193)(157,192)(158,194)(159,207)(160,209)(161,208)(162,210)(163,211)(164,213)(165,212)(166,214)(167,215)(168,217)(169,216)(170,218)(171,195)(172,197)(173,196)(174,198)(175,199)(176,201)(177,200)(178,202)(179,203)(180,205)(181,204)(182,206); s3 := Sym(218)!( 3,199)( 4,202)( 5,201)( 6,200)( 7,203)( 8,206)( 9,205)( 10,204)( 11,195)( 12,198)( 13,197)( 14,196)( 15,191)( 16,194)( 17,193)( 18,192)( 19,183)( 20,186)( 21,185)( 22,184)( 23,187)( 24,190)( 25,189)( 26,188)( 27,207)( 28,210)( 29,209)( 30,208)( 31,211)( 32,214)( 33,213)( 34,212)( 35,215)( 36,218)( 37,217)( 38,216)( 39,163)( 40,166)( 41,165)( 42,164)( 43,167)( 44,170)( 45,169)( 46,168)( 47,159)( 48,162)( 49,161)( 50,160)( 51,155)( 52,158)( 53,157)( 54,156)( 55,147)( 56,150)( 57,149)( 58,148)( 59,151)( 60,154)( 61,153)( 62,152)( 63,171)( 64,174)( 65,173)( 66,172)( 67,175)( 68,178)( 69,177)( 70,176)( 71,179)( 72,182)( 73,181)( 74,180)( 75,127)( 76,130)( 77,129)( 78,128)( 79,131)( 80,134)( 81,133)( 82,132)( 83,123)( 84,126)( 85,125)( 86,124)( 87,119)( 88,122)( 89,121)( 90,120)( 91,111)( 92,114)( 93,113)( 94,112)( 95,115)( 96,118)( 97,117)( 98,116)( 99,135)(100,138)(101,137)(102,136)(103,139)(104,142)(105,141)(106,140)(107,143)(108,146)(109,145)(110,144); s4 := Sym(218)!( 7, 11)( 8, 12)( 9, 13)( 10, 14)( 15, 27)( 16, 28)( 17, 29)( 18, 30)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 31)( 24, 32)( 25, 33)( 26, 34)( 43, 47)( 44, 48)( 45, 49)( 46, 50)( 51, 63)( 52, 64)( 53, 65)( 54, 66)( 55, 71)( 56, 72)( 57, 73)( 58, 74)( 59, 67)( 60, 68)( 61, 69)( 62, 70)( 79, 83)( 80, 84)( 81, 85)( 82, 86)( 87, 99)( 88,100)( 89,101)( 90,102)( 91,107)( 92,108)( 93,109)( 94,110)( 95,103)( 96,104)( 97,105)( 98,106)(115,119)(116,120)(117,121)(118,122)(123,135)(124,136)(125,137)(126,138)(127,143)(128,144)(129,145)(130,146)(131,139)(132,140)(133,141)(134,142)(151,155)(152,156)(153,157)(154,158)(159,171)(160,172)(161,173)(162,174)(163,179)(164,180)(165,181)(166,182)(167,175)(168,176)(169,177)(170,178)(187,191)(188,192)(189,193)(190,194)(195,207)(196,208)(197,209)(198,210)(199,215)(200,216)(201,217)(202,218)(203,211)(204,212)(205,213)(206,214); 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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3 >;