Overview
- Group
- SmallGroup(1728,46116)
- Rank
- 4
- Schläfli Type
- {2,6,6}
- Vertices, edges, …
- 2, 72, 216, 72
- 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
4-fold
6-fold
8-fold
9-fold
12-fold
18-fold
24-fold
36-fold
72-fold
108-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 16, 17)( 19, 23)( 20, 25)( 21, 24)( 22, 26)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)( 39, 75)( 40, 77)( 41, 76)( 42, 78)( 43, 83)( 44, 85)( 45, 84)( 46, 86)( 47, 79)( 48, 81)( 49, 80)( 50, 82)( 51, 87)( 52, 89)( 53, 88)( 54, 90)( 55, 95)( 56, 97)( 57, 96)( 58, 98)( 59, 91)( 60, 93)( 61, 92)( 62, 94)( 63, 99)( 64,101)( 65,100)( 66,102)( 67,107)( 68,109)( 69,108)( 70,110)( 71,103)( 72,105)( 73,104)( 74,106)(112,113)(115,119)(116,121)(117,120)(118,122)(124,125)(127,131)(128,133)(129,132)(130,134)(136,137)(139,143)(140,145)(141,144)(142,146)(147,183)(148,185)(149,184)(150,186)(151,191)(152,193)(153,192)(154,194)(155,187)(156,189)(157,188)(158,190)(159,195)(160,197)(161,196)(162,198)(163,203)(164,205)(165,204)(166,206)(167,199)(168,201)(169,200)(170,202)(171,207)(172,209)(173,208)(174,210)(175,215)(176,217)(177,216)(178,218)(179,211)(180,213)(181,212)(182,214);; s2 := ( 3, 39)( 4, 40)( 5, 42)( 6, 41)( 7, 43)( 8, 44)( 9, 46)( 10, 45)( 11, 47)( 12, 48)( 13, 50)( 14, 49)( 15, 71)( 16, 72)( 17, 74)( 18, 73)( 19, 63)( 20, 64)( 21, 66)( 22, 65)( 23, 67)( 24, 68)( 25, 70)( 26, 69)( 27, 55)( 28, 56)( 29, 58)( 30, 57)( 31, 59)( 32, 60)( 33, 62)( 34, 61)( 35, 51)( 36, 52)( 37, 54)( 38, 53)( 77, 78)( 81, 82)( 85, 86)( 87,107)( 88,108)( 89,110)( 90,109)( 91, 99)( 92,100)( 93,102)( 94,101)( 95,103)( 96,104)( 97,106)( 98,105)(111,147)(112,148)(113,150)(114,149)(115,151)(116,152)(117,154)(118,153)(119,155)(120,156)(121,158)(122,157)(123,179)(124,180)(125,182)(126,181)(127,171)(128,172)(129,174)(130,173)(131,175)(132,176)(133,178)(134,177)(135,163)(136,164)(137,166)(138,165)(139,167)(140,168)(141,170)(142,169)(143,159)(144,160)(145,162)(146,161)(185,186)(189,190)(193,194)(195,215)(196,216)(197,218)(198,217)(199,207)(200,208)(201,210)(202,209)(203,211)(204,212)(205,214)(206,213);; s3 := ( 3,126)( 4,124)( 5,125)( 6,123)( 7,130)( 8,128)( 9,129)( 10,127)( 11,134)( 12,132)( 13,133)( 14,131)( 15,114)( 16,112)( 17,113)( 18,111)( 19,118)( 20,116)( 21,117)( 22,115)( 23,122)( 24,120)( 25,121)( 26,119)( 27,138)( 28,136)( 29,137)( 30,135)( 31,142)( 32,140)( 33,141)( 34,139)( 35,146)( 36,144)( 37,145)( 38,143)( 39,198)( 40,196)( 41,197)( 42,195)( 43,202)( 44,200)( 45,201)( 46,199)( 47,206)( 48,204)( 49,205)( 50,203)( 51,186)( 52,184)( 53,185)( 54,183)( 55,190)( 56,188)( 57,189)( 58,187)( 59,194)( 60,192)( 61,193)( 62,191)( 63,210)( 64,208)( 65,209)( 66,207)( 67,214)( 68,212)( 69,213)( 70,211)( 71,218)( 72,216)( 73,217)( 74,215)( 75,162)( 76,160)( 77,161)( 78,159)( 79,166)( 80,164)( 81,165)( 82,163)( 83,170)( 84,168)( 85,169)( 86,167)( 87,150)( 88,148)( 89,149)( 90,147)( 91,154)( 92,152)( 93,153)( 94,151)( 95,158)( 96,156)( 97,157)( 98,155)( 99,174)(100,172)(101,173)(102,171)(103,178)(104,176)(105,177)(106,175)(107,182)(108,180)(109,181)(110,179);; 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(218)!(1,2); s1 := Sym(218)!( 4, 5)( 7, 11)( 8, 13)( 9, 12)( 10, 14)( 16, 17)( 19, 23)( 20, 25)( 21, 24)( 22, 26)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)( 39, 75)( 40, 77)( 41, 76)( 42, 78)( 43, 83)( 44, 85)( 45, 84)( 46, 86)( 47, 79)( 48, 81)( 49, 80)( 50, 82)( 51, 87)( 52, 89)( 53, 88)( 54, 90)( 55, 95)( 56, 97)( 57, 96)( 58, 98)( 59, 91)( 60, 93)( 61, 92)( 62, 94)( 63, 99)( 64,101)( 65,100)( 66,102)( 67,107)( 68,109)( 69,108)( 70,110)( 71,103)( 72,105)( 73,104)( 74,106)(112,113)(115,119)(116,121)(117,120)(118,122)(124,125)(127,131)(128,133)(129,132)(130,134)(136,137)(139,143)(140,145)(141,144)(142,146)(147,183)(148,185)(149,184)(150,186)(151,191)(152,193)(153,192)(154,194)(155,187)(156,189)(157,188)(158,190)(159,195)(160,197)(161,196)(162,198)(163,203)(164,205)(165,204)(166,206)(167,199)(168,201)(169,200)(170,202)(171,207)(172,209)(173,208)(174,210)(175,215)(176,217)(177,216)(178,218)(179,211)(180,213)(181,212)(182,214); s2 := Sym(218)!( 3, 39)( 4, 40)( 5, 42)( 6, 41)( 7, 43)( 8, 44)( 9, 46)( 10, 45)( 11, 47)( 12, 48)( 13, 50)( 14, 49)( 15, 71)( 16, 72)( 17, 74)( 18, 73)( 19, 63)( 20, 64)( 21, 66)( 22, 65)( 23, 67)( 24, 68)( 25, 70)( 26, 69)( 27, 55)( 28, 56)( 29, 58)( 30, 57)( 31, 59)( 32, 60)( 33, 62)( 34, 61)( 35, 51)( 36, 52)( 37, 54)( 38, 53)( 77, 78)( 81, 82)( 85, 86)( 87,107)( 88,108)( 89,110)( 90,109)( 91, 99)( 92,100)( 93,102)( 94,101)( 95,103)( 96,104)( 97,106)( 98,105)(111,147)(112,148)(113,150)(114,149)(115,151)(116,152)(117,154)(118,153)(119,155)(120,156)(121,158)(122,157)(123,179)(124,180)(125,182)(126,181)(127,171)(128,172)(129,174)(130,173)(131,175)(132,176)(133,178)(134,177)(135,163)(136,164)(137,166)(138,165)(139,167)(140,168)(141,170)(142,169)(143,159)(144,160)(145,162)(146,161)(185,186)(189,190)(193,194)(195,215)(196,216)(197,218)(198,217)(199,207)(200,208)(201,210)(202,209)(203,211)(204,212)(205,214)(206,213); s3 := Sym(218)!( 3,126)( 4,124)( 5,125)( 6,123)( 7,130)( 8,128)( 9,129)( 10,127)( 11,134)( 12,132)( 13,133)( 14,131)( 15,114)( 16,112)( 17,113)( 18,111)( 19,118)( 20,116)( 21,117)( 22,115)( 23,122)( 24,120)( 25,121)( 26,119)( 27,138)( 28,136)( 29,137)( 30,135)( 31,142)( 32,140)( 33,141)( 34,139)( 35,146)( 36,144)( 37,145)( 38,143)( 39,198)( 40,196)( 41,197)( 42,195)( 43,202)( 44,200)( 45,201)( 46,199)( 47,206)( 48,204)( 49,205)( 50,203)( 51,186)( 52,184)( 53,185)( 54,183)( 55,190)( 56,188)( 57,189)( 58,187)( 59,194)( 60,192)( 61,193)( 62,191)( 63,210)( 64,208)( 65,209)( 66,207)( 67,214)( 68,212)( 69,213)( 70,211)( 71,218)( 72,216)( 73,217)( 74,215)( 75,162)( 76,160)( 77,161)( 78,159)( 79,166)( 80,164)( 81,165)( 82,163)( 83,170)( 84,168)( 85,169)( 86,167)( 87,150)( 88,148)( 89,149)( 90,147)( 91,154)( 92,152)( 93,153)( 94,151)( 95,158)( 96,156)( 97,157)( 98,155)( 99,174)(100,172)(101,173)(102,171)(103,178)(104,176)(105,177)(106,175)(107,182)(108,180)(109,181)(110,179); 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2 >;