Overview
- Group
- SmallGroup(1728,46611)
- Rank
- 4
- Schläfli Type
- {4,12,2}
- Vertices, edges, …
- 36, 216, 108, 2
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 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
6-fold
9-fold
12-fold
18-fold
27-fold
36-fold
54-fold
72-fold
108-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 4, 22)( 5, 23)( 6, 24)( 7, 16)( 8, 17)( 9, 18)( 10, 19)( 11, 20)( 12, 21)( 31, 49)( 32, 50)( 33, 51)( 34, 43)( 35, 44)( 36, 45)( 37, 46)( 38, 47)( 39, 48)( 58, 76)( 59, 77)( 60, 78)( 61, 70)( 62, 71)( 63, 72)( 64, 73)( 65, 74)( 66, 75)( 85,103)( 86,104)( 87,105)( 88, 97)( 89, 98)( 90, 99)( 91,100)( 92,101)( 93,102)(109,163)(110,164)(111,165)(112,184)(113,185)(114,186)(115,178)(116,179)(117,180)(118,181)(119,182)(120,183)(121,175)(122,176)(123,177)(124,169)(125,170)(126,171)(127,172)(128,173)(129,174)(130,166)(131,167)(132,168)(133,187)(134,188)(135,189)(136,190)(137,191)(138,192)(139,211)(140,212)(141,213)(142,205)(143,206)(144,207)(145,208)(146,209)(147,210)(148,202)(149,203)(150,204)(151,196)(152,197)(153,198)(154,199)(155,200)(156,201)(157,193)(158,194)(159,195)(160,214)(161,215)(162,216);; s1 := ( 1,109)( 2,111)( 3,110)( 4,112)( 5,114)( 6,113)( 7,115)( 8,117)( 9,116)( 10,133)( 11,135)( 12,134)( 13,127)( 14,129)( 15,128)( 16,130)( 17,132)( 18,131)( 19,121)( 20,123)( 21,122)( 22,124)( 23,126)( 24,125)( 25,118)( 26,120)( 27,119)( 28,136)( 29,138)( 30,137)( 31,139)( 32,141)( 33,140)( 34,142)( 35,144)( 36,143)( 37,160)( 38,162)( 39,161)( 40,154)( 41,156)( 42,155)( 43,157)( 44,159)( 45,158)( 46,148)( 47,150)( 48,149)( 49,151)( 50,153)( 51,152)( 52,145)( 53,147)( 54,146)( 55,163)( 56,165)( 57,164)( 58,166)( 59,168)( 60,167)( 61,169)( 62,171)( 63,170)( 64,187)( 65,189)( 66,188)( 67,181)( 68,183)( 69,182)( 70,184)( 71,186)( 72,185)( 73,175)( 74,177)( 75,176)( 76,178)( 77,180)( 78,179)( 79,172)( 80,174)( 81,173)( 82,190)( 83,192)( 84,191)( 85,193)( 86,195)( 87,194)( 88,196)( 89,198)( 90,197)( 91,214)( 92,216)( 93,215)( 94,208)( 95,210)( 96,209)( 97,211)( 98,213)( 99,212)(100,202)(101,204)(102,203)(103,205)(104,207)(105,206)(106,199)(107,201)(108,200);; s2 := ( 1, 68)( 2, 67)( 3, 69)( 4, 74)( 5, 73)( 6, 75)( 7, 62)( 8, 61)( 9, 63)( 10, 77)( 11, 76)( 12, 78)( 13, 56)( 14, 55)( 15, 57)( 16, 71)( 17, 70)( 18, 72)( 19, 59)( 20, 58)( 21, 60)( 22, 65)( 23, 64)( 24, 66)( 25, 80)( 26, 79)( 27, 81)( 28, 95)( 29, 94)( 30, 96)( 31,101)( 32,100)( 33,102)( 34, 89)( 35, 88)( 36, 90)( 37,104)( 38,103)( 39,105)( 40, 83)( 41, 82)( 42, 84)( 43, 98)( 44, 97)( 45, 99)( 46, 86)( 47, 85)( 48, 87)( 49, 92)( 50, 91)( 51, 93)( 52,107)( 53,106)( 54,108)(109,149)(110,148)(111,150)(112,155)(113,154)(114,156)(115,143)(116,142)(117,144)(118,158)(119,157)(120,159)(121,137)(122,136)(123,138)(124,152)(125,151)(126,153)(127,140)(128,139)(129,141)(130,146)(131,145)(132,147)(133,161)(134,160)(135,162)(163,203)(164,202)(165,204)(166,209)(167,208)(168,210)(169,197)(170,196)(171,198)(172,212)(173,211)(174,213)(175,191)(176,190)(177,192)(178,206)(179,205)(180,207)(181,194)(182,193)(183,195)(184,200)(185,199)(186,201)(187,215)(188,214)(189,216);; s3 := (217,218);; 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, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(218)!( 4, 22)( 5, 23)( 6, 24)( 7, 16)( 8, 17)( 9, 18)( 10, 19)( 11, 20)( 12, 21)( 31, 49)( 32, 50)( 33, 51)( 34, 43)( 35, 44)( 36, 45)( 37, 46)( 38, 47)( 39, 48)( 58, 76)( 59, 77)( 60, 78)( 61, 70)( 62, 71)( 63, 72)( 64, 73)( 65, 74)( 66, 75)( 85,103)( 86,104)( 87,105)( 88, 97)( 89, 98)( 90, 99)( 91,100)( 92,101)( 93,102)(109,163)(110,164)(111,165)(112,184)(113,185)(114,186)(115,178)(116,179)(117,180)(118,181)(119,182)(120,183)(121,175)(122,176)(123,177)(124,169)(125,170)(126,171)(127,172)(128,173)(129,174)(130,166)(131,167)(132,168)(133,187)(134,188)(135,189)(136,190)(137,191)(138,192)(139,211)(140,212)(141,213)(142,205)(143,206)(144,207)(145,208)(146,209)(147,210)(148,202)(149,203)(150,204)(151,196)(152,197)(153,198)(154,199)(155,200)(156,201)(157,193)(158,194)(159,195)(160,214)(161,215)(162,216); s1 := Sym(218)!( 1,109)( 2,111)( 3,110)( 4,112)( 5,114)( 6,113)( 7,115)( 8,117)( 9,116)( 10,133)( 11,135)( 12,134)( 13,127)( 14,129)( 15,128)( 16,130)( 17,132)( 18,131)( 19,121)( 20,123)( 21,122)( 22,124)( 23,126)( 24,125)( 25,118)( 26,120)( 27,119)( 28,136)( 29,138)( 30,137)( 31,139)( 32,141)( 33,140)( 34,142)( 35,144)( 36,143)( 37,160)( 38,162)( 39,161)( 40,154)( 41,156)( 42,155)( 43,157)( 44,159)( 45,158)( 46,148)( 47,150)( 48,149)( 49,151)( 50,153)( 51,152)( 52,145)( 53,147)( 54,146)( 55,163)( 56,165)( 57,164)( 58,166)( 59,168)( 60,167)( 61,169)( 62,171)( 63,170)( 64,187)( 65,189)( 66,188)( 67,181)( 68,183)( 69,182)( 70,184)( 71,186)( 72,185)( 73,175)( 74,177)( 75,176)( 76,178)( 77,180)( 78,179)( 79,172)( 80,174)( 81,173)( 82,190)( 83,192)( 84,191)( 85,193)( 86,195)( 87,194)( 88,196)( 89,198)( 90,197)( 91,214)( 92,216)( 93,215)( 94,208)( 95,210)( 96,209)( 97,211)( 98,213)( 99,212)(100,202)(101,204)(102,203)(103,205)(104,207)(105,206)(106,199)(107,201)(108,200); s2 := Sym(218)!( 1, 68)( 2, 67)( 3, 69)( 4, 74)( 5, 73)( 6, 75)( 7, 62)( 8, 61)( 9, 63)( 10, 77)( 11, 76)( 12, 78)( 13, 56)( 14, 55)( 15, 57)( 16, 71)( 17, 70)( 18, 72)( 19, 59)( 20, 58)( 21, 60)( 22, 65)( 23, 64)( 24, 66)( 25, 80)( 26, 79)( 27, 81)( 28, 95)( 29, 94)( 30, 96)( 31,101)( 32,100)( 33,102)( 34, 89)( 35, 88)( 36, 90)( 37,104)( 38,103)( 39,105)( 40, 83)( 41, 82)( 42, 84)( 43, 98)( 44, 97)( 45, 99)( 46, 86)( 47, 85)( 48, 87)( 49, 92)( 50, 91)( 51, 93)( 52,107)( 53,106)( 54,108)(109,149)(110,148)(111,150)(112,155)(113,154)(114,156)(115,143)(116,142)(117,144)(118,158)(119,157)(120,159)(121,137)(122,136)(123,138)(124,152)(125,151)(126,153)(127,140)(128,139)(129,141)(130,146)(131,145)(132,147)(133,161)(134,160)(135,162)(163,203)(164,202)(165,204)(166,209)(167,208)(168,210)(169,197)(170,196)(171,198)(172,212)(173,211)(174,213)(175,191)(176,190)(177,192)(178,206)(179,205)(180,207)(181,194)(182,193)(183,195)(184,200)(185,199)(186,201)(187,215)(188,214)(189,216); s3 := Sym(218)!(217,218); poly := sub<Sym(218)|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, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*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 >;