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