Overview
- Group
- SmallGroup(1728,30882)
- Rank
- 5
- Schläfli Type
- {2,4,6,6}
- Vertices, edges, …
- 2, 4, 36, 54, 18
- Order of s0s1s2s3s4
- 12
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
9-fold
12-fold
18-fold
27-fold
36-fold
54-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3, 57)( 4, 58)( 5, 59)( 6, 60)( 7, 61)( 8, 62)( 9, 63)( 10, 64)( 11, 65)( 12, 66)( 13, 67)( 14, 68)( 15, 69)( 16, 70)( 17, 71)( 18, 72)( 19, 73)( 20, 74)( 21, 75)( 22, 76)( 23, 77)( 24, 78)( 25, 79)( 26, 80)( 27, 81)( 28, 82)( 29, 83)( 30, 84)( 31, 85)( 32, 86)( 33, 87)( 34, 88)( 35, 89)( 36, 90)( 37, 91)( 38, 92)( 39, 93)( 40, 94)( 41, 95)( 42, 96)( 43, 97)( 44, 98)( 45, 99)( 46,100)( 47,101)( 48,102)( 49,103)( 50,104)( 51,105)( 52,106)( 53,107)( 54,108)( 55,109)( 56,110)(111,165)(112,166)(113,167)(114,168)(115,169)(116,170)(117,171)(118,172)(119,173)(120,174)(121,175)(122,176)(123,177)(124,178)(125,179)(126,180)(127,181)(128,182)(129,183)(130,184)(131,185)(132,186)(133,187)(134,188)(135,189)(136,190)(137,191)(138,192)(139,193)(140,194)(141,195)(142,196)(143,197)(144,198)(145,199)(146,200)(147,201)(148,202)(149,203)(150,204)(151,205)(152,206)(153,207)(154,208)(155,209)(156,210)(157,211)(158,212)(159,213)(160,214)(161,215)(162,216)(163,217)(164,218);; s2 := ( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)( 35, 37)( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)( 53, 55)( 57, 84)( 58, 86)( 59, 85)( 60, 90)( 61, 92)( 62, 91)( 63, 87)( 64, 89)( 65, 88)( 66, 93)( 67, 95)( 68, 94)( 69, 99)( 70,101)( 71,100)( 72, 96)( 73, 98)( 74, 97)( 75,102)( 76,104)( 77,103)( 78,108)( 79,110)( 80,109)( 81,105)( 82,107)( 83,106)(112,113)(114,117)(115,119)(116,118)(121,122)(123,126)(124,128)(125,127)(130,131)(132,135)(133,137)(134,136)(139,140)(141,144)(142,146)(143,145)(148,149)(150,153)(151,155)(152,154)(157,158)(159,162)(160,164)(161,163)(165,192)(166,194)(167,193)(168,198)(169,200)(170,199)(171,195)(172,197)(173,196)(174,201)(175,203)(176,202)(177,207)(178,209)(179,208)(180,204)(181,206)(182,205)(183,210)(184,212)(185,211)(186,216)(187,218)(188,217)(189,213)(190,215)(191,214);; s3 := ( 3, 6)( 4, 7)( 5, 8)( 12, 24)( 13, 25)( 14, 26)( 15, 21)( 16, 22)( 17, 23)( 18, 27)( 19, 28)( 20, 29)( 30, 33)( 31, 34)( 32, 35)( 39, 51)( 40, 52)( 41, 53)( 42, 48)( 43, 49)( 44, 50)( 45, 54)( 46, 55)( 47, 56)( 57, 60)( 58, 61)( 59, 62)( 66, 78)( 67, 79)( 68, 80)( 69, 75)( 70, 76)( 71, 77)( 72, 81)( 73, 82)( 74, 83)( 84, 87)( 85, 88)( 86, 89)( 93,105)( 94,106)( 95,107)( 96,102)( 97,103)( 98,104)( 99,108)(100,109)(101,110)(111,114)(112,115)(113,116)(120,132)(121,133)(122,134)(123,129)(124,130)(125,131)(126,135)(127,136)(128,137)(138,141)(139,142)(140,143)(147,159)(148,160)(149,161)(150,156)(151,157)(152,158)(153,162)(154,163)(155,164)(165,168)(166,169)(167,170)(174,186)(175,187)(176,188)(177,183)(178,184)(179,185)(180,189)(181,190)(182,191)(192,195)(193,196)(194,197)(201,213)(202,214)(203,215)(204,210)(205,211)(206,212)(207,216)(208,217)(209,218);; s4 := ( 3,120)( 4,121)( 5,122)( 6,128)( 7,126)( 8,127)( 9,124)( 10,125)( 11,123)( 12,111)( 13,112)( 14,113)( 15,119)( 16,117)( 17,118)( 18,115)( 19,116)( 20,114)( 21,129)( 22,130)( 23,131)( 24,137)( 25,135)( 26,136)( 27,133)( 28,134)( 29,132)( 30,147)( 31,148)( 32,149)( 33,155)( 34,153)( 35,154)( 36,151)( 37,152)( 38,150)( 39,138)( 40,139)( 41,140)( 42,146)( 43,144)( 44,145)( 45,142)( 46,143)( 47,141)( 48,156)( 49,157)( 50,158)( 51,164)( 52,162)( 53,163)( 54,160)( 55,161)( 56,159)( 57,174)( 58,175)( 59,176)( 60,182)( 61,180)( 62,181)( 63,178)( 64,179)( 65,177)( 66,165)( 67,166)( 68,167)( 69,173)( 70,171)( 71,172)( 72,169)( 73,170)( 74,168)( 75,183)( 76,184)( 77,185)( 78,191)( 79,189)( 80,190)( 81,187)( 82,188)( 83,186)( 84,201)( 85,202)( 86,203)( 87,209)( 88,207)( 89,208)( 90,205)( 91,206)( 92,204)( 93,192)( 94,193)( 95,194)( 96,200)( 97,198)( 98,199)( 99,196)(100,197)(101,195)(102,210)(103,211)(104,212)(105,218)(106,216)(107,217)(108,214)(109,215)(110,213);; 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*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s4*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(218)!(1,2); s1 := Sym(218)!( 3, 57)( 4, 58)( 5, 59)( 6, 60)( 7, 61)( 8, 62)( 9, 63)( 10, 64)( 11, 65)( 12, 66)( 13, 67)( 14, 68)( 15, 69)( 16, 70)( 17, 71)( 18, 72)( 19, 73)( 20, 74)( 21, 75)( 22, 76)( 23, 77)( 24, 78)( 25, 79)( 26, 80)( 27, 81)( 28, 82)( 29, 83)( 30, 84)( 31, 85)( 32, 86)( 33, 87)( 34, 88)( 35, 89)( 36, 90)( 37, 91)( 38, 92)( 39, 93)( 40, 94)( 41, 95)( 42, 96)( 43, 97)( 44, 98)( 45, 99)( 46,100)( 47,101)( 48,102)( 49,103)( 50,104)( 51,105)( 52,106)( 53,107)( 54,108)( 55,109)( 56,110)(111,165)(112,166)(113,167)(114,168)(115,169)(116,170)(117,171)(118,172)(119,173)(120,174)(121,175)(122,176)(123,177)(124,178)(125,179)(126,180)(127,181)(128,182)(129,183)(130,184)(131,185)(132,186)(133,187)(134,188)(135,189)(136,190)(137,191)(138,192)(139,193)(140,194)(141,195)(142,196)(143,197)(144,198)(145,199)(146,200)(147,201)(148,202)(149,203)(150,204)(151,205)(152,206)(153,207)(154,208)(155,209)(156,210)(157,211)(158,212)(159,213)(160,214)(161,215)(162,216)(163,217)(164,218); s2 := Sym(218)!( 4, 5)( 6, 9)( 7, 11)( 8, 10)( 13, 14)( 15, 18)( 16, 20)( 17, 19)( 22, 23)( 24, 27)( 25, 29)( 26, 28)( 31, 32)( 33, 36)( 34, 38)( 35, 37)( 40, 41)( 42, 45)( 43, 47)( 44, 46)( 49, 50)( 51, 54)( 52, 56)( 53, 55)( 57, 84)( 58, 86)( 59, 85)( 60, 90)( 61, 92)( 62, 91)( 63, 87)( 64, 89)( 65, 88)( 66, 93)( 67, 95)( 68, 94)( 69, 99)( 70,101)( 71,100)( 72, 96)( 73, 98)( 74, 97)( 75,102)( 76,104)( 77,103)( 78,108)( 79,110)( 80,109)( 81,105)( 82,107)( 83,106)(112,113)(114,117)(115,119)(116,118)(121,122)(123,126)(124,128)(125,127)(130,131)(132,135)(133,137)(134,136)(139,140)(141,144)(142,146)(143,145)(148,149)(150,153)(151,155)(152,154)(157,158)(159,162)(160,164)(161,163)(165,192)(166,194)(167,193)(168,198)(169,200)(170,199)(171,195)(172,197)(173,196)(174,201)(175,203)(176,202)(177,207)(178,209)(179,208)(180,204)(181,206)(182,205)(183,210)(184,212)(185,211)(186,216)(187,218)(188,217)(189,213)(190,215)(191,214); s3 := Sym(218)!( 3, 6)( 4, 7)( 5, 8)( 12, 24)( 13, 25)( 14, 26)( 15, 21)( 16, 22)( 17, 23)( 18, 27)( 19, 28)( 20, 29)( 30, 33)( 31, 34)( 32, 35)( 39, 51)( 40, 52)( 41, 53)( 42, 48)( 43, 49)( 44, 50)( 45, 54)( 46, 55)( 47, 56)( 57, 60)( 58, 61)( 59, 62)( 66, 78)( 67, 79)( 68, 80)( 69, 75)( 70, 76)( 71, 77)( 72, 81)( 73, 82)( 74, 83)( 84, 87)( 85, 88)( 86, 89)( 93,105)( 94,106)( 95,107)( 96,102)( 97,103)( 98,104)( 99,108)(100,109)(101,110)(111,114)(112,115)(113,116)(120,132)(121,133)(122,134)(123,129)(124,130)(125,131)(126,135)(127,136)(128,137)(138,141)(139,142)(140,143)(147,159)(148,160)(149,161)(150,156)(151,157)(152,158)(153,162)(154,163)(155,164)(165,168)(166,169)(167,170)(174,186)(175,187)(176,188)(177,183)(178,184)(179,185)(180,189)(181,190)(182,191)(192,195)(193,196)(194,197)(201,213)(202,214)(203,215)(204,210)(205,211)(206,212)(207,216)(208,217)(209,218); s4 := Sym(218)!( 3,120)( 4,121)( 5,122)( 6,128)( 7,126)( 8,127)( 9,124)( 10,125)( 11,123)( 12,111)( 13,112)( 14,113)( 15,119)( 16,117)( 17,118)( 18,115)( 19,116)( 20,114)( 21,129)( 22,130)( 23,131)( 24,137)( 25,135)( 26,136)( 27,133)( 28,134)( 29,132)( 30,147)( 31,148)( 32,149)( 33,155)( 34,153)( 35,154)( 36,151)( 37,152)( 38,150)( 39,138)( 40,139)( 41,140)( 42,146)( 43,144)( 44,145)( 45,142)( 46,143)( 47,141)( 48,156)( 49,157)( 50,158)( 51,164)( 52,162)( 53,163)( 54,160)( 55,161)( 56,159)( 57,174)( 58,175)( 59,176)( 60,182)( 61,180)( 62,181)( 63,178)( 64,179)( 65,177)( 66,165)( 67,166)( 68,167)( 69,173)( 70,171)( 71,172)( 72,169)( 73,170)( 74,168)( 75,183)( 76,184)( 77,185)( 78,191)( 79,189)( 80,190)( 81,187)( 82,188)( 83,186)( 84,201)( 85,202)( 86,203)( 87,209)( 88,207)( 89,208)( 90,205)( 91,206)( 92,204)( 93,192)( 94,193)( 95,194)( 96,200)( 97,198)( 98,199)( 99,196)(100,197)(101,195)(102,210)(103,211)(104,212)(105,218)(106,216)(107,217)(108,214)(109,215)(110,213); 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*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s4*s3*s2 >;