Overview
- Group
- SmallGroup(1728,15830)
- Rank
- 4
- Schläfli Type
- {2,24,18}
- Vertices, edges, …
- 2, 24, 216, 18
- Order of s0s1s2s3
- 72
- 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
4-fold
6-fold
9-fold
12-fold
18-fold
24-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 := (1,2);; s1 := ( 12, 21)( 13, 22)( 14, 23)( 15, 24)( 16, 25)( 17, 26)( 18, 27)( 19, 28)( 20, 29)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)( 46, 55)( 47, 56)( 57, 84)( 58, 85)( 59, 86)( 60, 87)( 61, 88)( 62, 89)( 63, 90)( 64, 91)( 65, 92)( 66,102)( 67,103)( 68,104)( 69,105)( 70,106)( 71,107)( 72,108)( 73,109)( 74,110)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 99)( 82,100)( 83,101)(111,165)(112,166)(113,167)(114,168)(115,169)(116,170)(117,171)(118,172)(119,173)(120,183)(121,184)(122,185)(123,186)(124,187)(125,188)(126,189)(127,190)(128,191)(129,174)(130,175)(131,176)(132,177)(133,178)(134,179)(135,180)(136,181)(137,182)(138,192)(139,193)(140,194)(141,195)(142,196)(143,197)(144,198)(145,199)(146,200)(147,210)(148,211)(149,212)(150,213)(151,214)(152,215)(153,216)(154,217)(155,218)(156,201)(157,202)(158,203)(159,204)(160,205)(161,206)(162,207)(163,208)(164,209);; s2 := ( 3,120)( 4,122)( 5,121)( 6,128)( 7,127)( 8,126)( 9,125)( 10,124)( 11,123)( 12,111)( 13,113)( 14,112)( 15,119)( 16,118)( 17,117)( 18,116)( 19,115)( 20,114)( 21,129)( 22,131)( 23,130)( 24,137)( 25,136)( 26,135)( 27,134)( 28,133)( 29,132)( 30,147)( 31,149)( 32,148)( 33,155)( 34,154)( 35,153)( 36,152)( 37,151)( 38,150)( 39,138)( 40,140)( 41,139)( 42,146)( 43,145)( 44,144)( 45,143)( 46,142)( 47,141)( 48,156)( 49,158)( 50,157)( 51,164)( 52,163)( 53,162)( 54,161)( 55,160)( 56,159)( 57,201)( 58,203)( 59,202)( 60,209)( 61,208)( 62,207)( 63,206)( 64,205)( 65,204)( 66,192)( 67,194)( 68,193)( 69,200)( 70,199)( 71,198)( 72,197)( 73,196)( 74,195)( 75,210)( 76,212)( 77,211)( 78,218)( 79,217)( 80,216)( 81,215)( 82,214)( 83,213)( 84,174)( 85,176)( 86,175)( 87,182)( 88,181)( 89,180)( 90,179)( 91,178)( 92,177)( 93,165)( 94,167)( 95,166)( 96,173)( 97,172)( 98,171)( 99,170)(100,169)(101,168)(102,183)(103,185)(104,184)(105,191)(106,190)(107,189)(108,188)(109,187)(110,186);; s3 := ( 3, 6)( 4, 8)( 5, 7)( 9, 11)( 12, 15)( 13, 17)( 14, 16)( 18, 20)( 21, 24)( 22, 26)( 23, 25)( 27, 29)( 30, 33)( 31, 35)( 32, 34)( 36, 38)( 39, 42)( 40, 44)( 41, 43)( 45, 47)( 48, 51)( 49, 53)( 50, 52)( 54, 56)( 57, 60)( 58, 62)( 59, 61)( 63, 65)( 66, 69)( 67, 71)( 68, 70)( 72, 74)( 75, 78)( 76, 80)( 77, 79)( 81, 83)( 84, 87)( 85, 89)( 86, 88)( 90, 92)( 93, 96)( 94, 98)( 95, 97)( 99,101)(102,105)(103,107)(104,106)(108,110)(111,114)(112,116)(113,115)(117,119)(120,123)(121,125)(122,124)(126,128)(129,132)(130,134)(131,133)(135,137)(138,141)(139,143)(140,142)(144,146)(147,150)(148,152)(149,151)(153,155)(156,159)(157,161)(158,160)(162,164)(165,168)(166,170)(167,169)(171,173)(174,177)(175,179)(176,178)(180,182)(183,186)(184,188)(185,187)(189,191)(192,195)(193,197)(194,196)(198,200)(201,204)(202,206)(203,205)(207,209)(210,213)(211,215)(212,214)(216,218);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!(1,2); s1 := Sym(218)!( 12, 21)( 13, 22)( 14, 23)( 15, 24)( 16, 25)( 17, 26)( 18, 27)( 19, 28)( 20, 29)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)( 46, 55)( 47, 56)( 57, 84)( 58, 85)( 59, 86)( 60, 87)( 61, 88)( 62, 89)( 63, 90)( 64, 91)( 65, 92)( 66,102)( 67,103)( 68,104)( 69,105)( 70,106)( 71,107)( 72,108)( 73,109)( 74,110)( 75, 93)( 76, 94)( 77, 95)( 78, 96)( 79, 97)( 80, 98)( 81, 99)( 82,100)( 83,101)(111,165)(112,166)(113,167)(114,168)(115,169)(116,170)(117,171)(118,172)(119,173)(120,183)(121,184)(122,185)(123,186)(124,187)(125,188)(126,189)(127,190)(128,191)(129,174)(130,175)(131,176)(132,177)(133,178)(134,179)(135,180)(136,181)(137,182)(138,192)(139,193)(140,194)(141,195)(142,196)(143,197)(144,198)(145,199)(146,200)(147,210)(148,211)(149,212)(150,213)(151,214)(152,215)(153,216)(154,217)(155,218)(156,201)(157,202)(158,203)(159,204)(160,205)(161,206)(162,207)(163,208)(164,209); s2 := Sym(218)!( 3,120)( 4,122)( 5,121)( 6,128)( 7,127)( 8,126)( 9,125)( 10,124)( 11,123)( 12,111)( 13,113)( 14,112)( 15,119)( 16,118)( 17,117)( 18,116)( 19,115)( 20,114)( 21,129)( 22,131)( 23,130)( 24,137)( 25,136)( 26,135)( 27,134)( 28,133)( 29,132)( 30,147)( 31,149)( 32,148)( 33,155)( 34,154)( 35,153)( 36,152)( 37,151)( 38,150)( 39,138)( 40,140)( 41,139)( 42,146)( 43,145)( 44,144)( 45,143)( 46,142)( 47,141)( 48,156)( 49,158)( 50,157)( 51,164)( 52,163)( 53,162)( 54,161)( 55,160)( 56,159)( 57,201)( 58,203)( 59,202)( 60,209)( 61,208)( 62,207)( 63,206)( 64,205)( 65,204)( 66,192)( 67,194)( 68,193)( 69,200)( 70,199)( 71,198)( 72,197)( 73,196)( 74,195)( 75,210)( 76,212)( 77,211)( 78,218)( 79,217)( 80,216)( 81,215)( 82,214)( 83,213)( 84,174)( 85,176)( 86,175)( 87,182)( 88,181)( 89,180)( 90,179)( 91,178)( 92,177)( 93,165)( 94,167)( 95,166)( 96,173)( 97,172)( 98,171)( 99,170)(100,169)(101,168)(102,183)(103,185)(104,184)(105,191)(106,190)(107,189)(108,188)(109,187)(110,186); s3 := Sym(218)!( 3, 6)( 4, 8)( 5, 7)( 9, 11)( 12, 15)( 13, 17)( 14, 16)( 18, 20)( 21, 24)( 22, 26)( 23, 25)( 27, 29)( 30, 33)( 31, 35)( 32, 34)( 36, 38)( 39, 42)( 40, 44)( 41, 43)( 45, 47)( 48, 51)( 49, 53)( 50, 52)( 54, 56)( 57, 60)( 58, 62)( 59, 61)( 63, 65)( 66, 69)( 67, 71)( 68, 70)( 72, 74)( 75, 78)( 76, 80)( 77, 79)( 81, 83)( 84, 87)( 85, 89)( 86, 88)( 90, 92)( 93, 96)( 94, 98)( 95, 97)( 99,101)(102,105)(103,107)(104,106)(108,110)(111,114)(112,116)(113,115)(117,119)(120,123)(121,125)(122,124)(126,128)(129,132)(130,134)(131,133)(135,137)(138,141)(139,143)(140,142)(144,146)(147,150)(148,152)(149,151)(153,155)(156,159)(157,161)(158,160)(162,164)(165,168)(166,170)(167,169)(171,173)(174,177)(175,179)(176,178)(180,182)(183,186)(184,188)(185,187)(189,191)(192,195)(193,197)(194,196)(198,200)(201,204)(202,206)(203,205)(207,209)(210,213)(211,215)(212,214)(216,218); 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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;