Overview
- Group
- SmallGroup(1728,20782)
- Rank
- 5
- Schläfli Type
- {27,4,2,2}
- Vertices, edges, …
- 54, 108, 8, 2, 2
- Order of s0s1s2s3s4
- 54
- 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
36-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 9)( 6, 11)( 7, 10)( 8, 12)( 13, 29)( 14, 31)( 15, 30)( 16, 32)( 17, 25)( 18, 27)( 19, 26)( 20, 28)( 21, 33)( 22, 35)( 23, 34)( 24, 36)( 37, 85)( 38, 87)( 39, 86)( 40, 88)( 41, 93)( 42, 95)( 43, 94)( 44, 96)( 45, 89)( 46, 91)( 47, 90)( 48, 92)( 49, 73)( 50, 75)( 51, 74)( 52, 76)( 53, 81)( 54, 83)( 55, 82)( 56, 84)( 57, 77)( 58, 79)( 59, 78)( 60, 80)( 61,101)( 62,103)( 63,102)( 64,104)( 65, 97)( 66, 99)( 67, 98)( 68,100)( 69,105)( 70,107)( 71,106)( 72,108)(110,111)(113,117)(114,119)(115,118)(116,120)(121,137)(122,139)(123,138)(124,140)(125,133)(126,135)(127,134)(128,136)(129,141)(130,143)(131,142)(132,144)(145,193)(146,195)(147,194)(148,196)(149,201)(150,203)(151,202)(152,204)(153,197)(154,199)(155,198)(156,200)(157,181)(158,183)(159,182)(160,184)(161,189)(162,191)(163,190)(164,192)(165,185)(166,187)(167,186)(168,188)(169,209)(170,211)(171,210)(172,212)(173,205)(174,207)(175,206)(176,208)(177,213)(178,215)(179,214)(180,216);; s1 := ( 1, 37)( 2, 38)( 3, 40)( 4, 39)( 5, 45)( 6, 46)( 7, 48)( 8, 47)( 9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 65)( 14, 66)( 15, 68)( 16, 67)( 17, 61)( 18, 62)( 19, 64)( 20, 63)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 53)( 26, 54)( 27, 56)( 28, 55)( 29, 49)( 30, 50)( 31, 52)( 32, 51)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 73, 85)( 74, 86)( 75, 88)( 76, 87)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 97,101)( 98,102)( 99,104)(100,103)(107,108)(109,145)(110,146)(111,148)(112,147)(113,153)(114,154)(115,156)(116,155)(117,149)(118,150)(119,152)(120,151)(121,173)(122,174)(123,176)(124,175)(125,169)(126,170)(127,172)(128,171)(129,177)(130,178)(131,180)(132,179)(133,161)(134,162)(135,164)(136,163)(137,157)(138,158)(139,160)(140,159)(141,165)(142,166)(143,168)(144,167)(181,193)(182,194)(183,196)(184,195)(185,201)(186,202)(187,204)(188,203)(189,197)(190,198)(191,200)(192,199)(205,209)(206,210)(207,212)(208,211)(215,216);; s2 := ( 1,112)( 2,111)( 3,110)( 4,109)( 5,116)( 6,115)( 7,114)( 8,113)( 9,120)( 10,119)( 11,118)( 12,117)( 13,124)( 14,123)( 15,122)( 16,121)( 17,128)( 18,127)( 19,126)( 20,125)( 21,132)( 22,131)( 23,130)( 24,129)( 25,136)( 26,135)( 27,134)( 28,133)( 29,140)( 30,139)( 31,138)( 32,137)( 33,144)( 34,143)( 35,142)( 36,141)( 37,148)( 38,147)( 39,146)( 40,145)( 41,152)( 42,151)( 43,150)( 44,149)( 45,156)( 46,155)( 47,154)( 48,153)( 49,160)( 50,159)( 51,158)( 52,157)( 53,164)( 54,163)( 55,162)( 56,161)( 57,168)( 58,167)( 59,166)( 60,165)( 61,172)( 62,171)( 63,170)( 64,169)( 65,176)( 66,175)( 67,174)( 68,173)( 69,180)( 70,179)( 71,178)( 72,177)( 73,184)( 74,183)( 75,182)( 76,181)( 77,188)( 78,187)( 79,186)( 80,185)( 81,192)( 82,191)( 83,190)( 84,189)( 85,196)( 86,195)( 87,194)( 88,193)( 89,200)( 90,199)( 91,198)( 92,197)( 93,204)( 94,203)( 95,202)( 96,201)( 97,208)( 98,207)( 99,206)(100,205)(101,212)(102,211)(103,210)(104,209)(105,216)(106,215)(107,214)(108,213);; s3 := (217,218);; s4 := (219,220);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(220)!( 2, 3)( 5, 9)( 6, 11)( 7, 10)( 8, 12)( 13, 29)( 14, 31)( 15, 30)( 16, 32)( 17, 25)( 18, 27)( 19, 26)( 20, 28)( 21, 33)( 22, 35)( 23, 34)( 24, 36)( 37, 85)( 38, 87)( 39, 86)( 40, 88)( 41, 93)( 42, 95)( 43, 94)( 44, 96)( 45, 89)( 46, 91)( 47, 90)( 48, 92)( 49, 73)( 50, 75)( 51, 74)( 52, 76)( 53, 81)( 54, 83)( 55, 82)( 56, 84)( 57, 77)( 58, 79)( 59, 78)( 60, 80)( 61,101)( 62,103)( 63,102)( 64,104)( 65, 97)( 66, 99)( 67, 98)( 68,100)( 69,105)( 70,107)( 71,106)( 72,108)(110,111)(113,117)(114,119)(115,118)(116,120)(121,137)(122,139)(123,138)(124,140)(125,133)(126,135)(127,134)(128,136)(129,141)(130,143)(131,142)(132,144)(145,193)(146,195)(147,194)(148,196)(149,201)(150,203)(151,202)(152,204)(153,197)(154,199)(155,198)(156,200)(157,181)(158,183)(159,182)(160,184)(161,189)(162,191)(163,190)(164,192)(165,185)(166,187)(167,186)(168,188)(169,209)(170,211)(171,210)(172,212)(173,205)(174,207)(175,206)(176,208)(177,213)(178,215)(179,214)(180,216); s1 := Sym(220)!( 1, 37)( 2, 38)( 3, 40)( 4, 39)( 5, 45)( 6, 46)( 7, 48)( 8, 47)( 9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 65)( 14, 66)( 15, 68)( 16, 67)( 17, 61)( 18, 62)( 19, 64)( 20, 63)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 53)( 26, 54)( 27, 56)( 28, 55)( 29, 49)( 30, 50)( 31, 52)( 32, 51)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 73, 85)( 74, 86)( 75, 88)( 76, 87)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 97,101)( 98,102)( 99,104)(100,103)(107,108)(109,145)(110,146)(111,148)(112,147)(113,153)(114,154)(115,156)(116,155)(117,149)(118,150)(119,152)(120,151)(121,173)(122,174)(123,176)(124,175)(125,169)(126,170)(127,172)(128,171)(129,177)(130,178)(131,180)(132,179)(133,161)(134,162)(135,164)(136,163)(137,157)(138,158)(139,160)(140,159)(141,165)(142,166)(143,168)(144,167)(181,193)(182,194)(183,196)(184,195)(185,201)(186,202)(187,204)(188,203)(189,197)(190,198)(191,200)(192,199)(205,209)(206,210)(207,212)(208,211)(215,216); s2 := Sym(220)!( 1,112)( 2,111)( 3,110)( 4,109)( 5,116)( 6,115)( 7,114)( 8,113)( 9,120)( 10,119)( 11,118)( 12,117)( 13,124)( 14,123)( 15,122)( 16,121)( 17,128)( 18,127)( 19,126)( 20,125)( 21,132)( 22,131)( 23,130)( 24,129)( 25,136)( 26,135)( 27,134)( 28,133)( 29,140)( 30,139)( 31,138)( 32,137)( 33,144)( 34,143)( 35,142)( 36,141)( 37,148)( 38,147)( 39,146)( 40,145)( 41,152)( 42,151)( 43,150)( 44,149)( 45,156)( 46,155)( 47,154)( 48,153)( 49,160)( 50,159)( 51,158)( 52,157)( 53,164)( 54,163)( 55,162)( 56,161)( 57,168)( 58,167)( 59,166)( 60,165)( 61,172)( 62,171)( 63,170)( 64,169)( 65,176)( 66,175)( 67,174)( 68,173)( 69,180)( 70,179)( 71,178)( 72,177)( 73,184)( 74,183)( 75,182)( 76,181)( 77,188)( 78,187)( 79,186)( 80,185)( 81,192)( 82,191)( 83,190)( 84,189)( 85,196)( 86,195)( 87,194)( 88,193)( 89,200)( 90,199)( 91,198)( 92,197)( 93,204)( 94,203)( 95,202)( 96,201)( 97,208)( 98,207)( 99,206)(100,205)(101,212)(102,211)(103,210)(104,209)(105,216)(106,215)(107,214)(108,213); s3 := Sym(220)!(217,218); s4 := Sym(220)!(219,220); poly := sub<Sym(220)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;