Overview
- Group
- SmallGroup(1728,46116)
- Rank
- 4
- Schläfli Type
- {2,12,6}
- Vertices, edges, …
- 2, 72, 216, 36
- Order of s0s1s2s3
- 6
- 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
36-fold
72-fold
108-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3, 5)( 4, 6)( 7, 13)( 8, 14)( 9, 11)( 10, 12)( 15, 29)( 16, 30)( 17, 27)( 18, 28)( 19, 37)( 20, 38)( 21, 35)( 22, 36)( 23, 33)( 24, 34)( 25, 31)( 26, 32)( 39, 41)( 40, 42)( 43, 49)( 44, 50)( 45, 47)( 46, 48)( 51, 65)( 52, 66)( 53, 63)( 54, 64)( 55, 73)( 56, 74)( 57, 71)( 58, 72)( 59, 69)( 60, 70)( 61, 67)( 62, 68)( 75, 77)( 76, 78)( 79, 85)( 80, 86)( 81, 83)( 82, 84)( 87,101)( 88,102)( 89, 99)( 90,100)( 91,109)( 92,110)( 93,107)( 94,108)( 95,105)( 96,106)( 97,103)( 98,104)(111,113)(112,114)(115,121)(116,122)(117,119)(118,120)(123,137)(124,138)(125,135)(126,136)(127,145)(128,146)(129,143)(130,144)(131,141)(132,142)(133,139)(134,140)(147,149)(148,150)(151,157)(152,158)(153,155)(154,156)(159,173)(160,174)(161,171)(162,172)(163,181)(164,182)(165,179)(166,180)(167,177)(168,178)(169,175)(170,176)(183,185)(184,186)(187,193)(188,194)(189,191)(190,192)(195,209)(196,210)(197,207)(198,208)(199,217)(200,218)(201,215)(202,216)(203,213)(204,214)(205,211)(206,212);; s2 := ( 3, 15)( 4, 17)( 5, 16)( 6, 18)( 7, 19)( 8, 21)( 9, 20)( 10, 22)( 11, 23)( 12, 25)( 13, 24)( 14, 26)( 28, 29)( 32, 33)( 36, 37)( 39, 87)( 40, 89)( 41, 88)( 42, 90)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 95)( 48, 97)( 49, 96)( 50, 98)( 51, 75)( 52, 77)( 53, 76)( 54, 78)( 55, 79)( 56, 81)( 57, 80)( 58, 82)( 59, 83)( 60, 85)( 61, 84)( 62, 86)( 63, 99)( 64,101)( 65,100)( 66,102)( 67,103)( 68,105)( 69,104)( 70,106)( 71,107)( 72,109)( 73,108)( 74,110)(111,123)(112,125)(113,124)(114,126)(115,127)(116,129)(117,128)(118,130)(119,131)(120,133)(121,132)(122,134)(136,137)(140,141)(144,145)(147,195)(148,197)(149,196)(150,198)(151,199)(152,201)(153,200)(154,202)(155,203)(156,205)(157,204)(158,206)(159,183)(160,185)(161,184)(162,186)(163,187)(164,189)(165,188)(166,190)(167,191)(168,193)(169,192)(170,194)(171,207)(172,209)(173,208)(174,210)(175,211)(176,213)(177,212)(178,214)(179,215)(180,217)(181,216)(182,218);; s3 := ( 3,183)( 4,186)( 5,185)( 6,184)( 7,191)( 8,194)( 9,193)( 10,192)( 11,187)( 12,190)( 13,189)( 14,188)( 15,203)( 16,206)( 17,205)( 18,204)( 19,199)( 20,202)( 21,201)( 22,200)( 23,195)( 24,198)( 25,197)( 26,196)( 27,211)( 28,214)( 29,213)( 30,212)( 31,207)( 32,210)( 33,209)( 34,208)( 35,215)( 36,218)( 37,217)( 38,216)( 39,147)( 40,150)( 41,149)( 42,148)( 43,155)( 44,158)( 45,157)( 46,156)( 47,151)( 48,154)( 49,153)( 50,152)( 51,167)( 52,170)( 53,169)( 54,168)( 55,163)( 56,166)( 57,165)( 58,164)( 59,159)( 60,162)( 61,161)( 62,160)( 63,175)( 64,178)( 65,177)( 66,176)( 67,171)( 68,174)( 69,173)( 70,172)( 71,179)( 72,182)( 73,181)( 74,180)( 75,111)( 76,114)( 77,113)( 78,112)( 79,119)( 80,122)( 81,121)( 82,120)( 83,115)( 84,118)( 85,117)( 86,116)( 87,131)( 88,134)( 89,133)( 90,132)( 91,127)( 92,130)( 93,129)( 94,128)( 95,123)( 96,126)( 97,125)( 98,124)( 99,139)(100,142)(101,141)(102,140)(103,135)(104,138)(105,137)(106,136)(107,143)(108,146)(109,145)(110,144);; 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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(218)!(1,2); s1 := Sym(218)!( 3, 5)( 4, 6)( 7, 13)( 8, 14)( 9, 11)( 10, 12)( 15, 29)( 16, 30)( 17, 27)( 18, 28)( 19, 37)( 20, 38)( 21, 35)( 22, 36)( 23, 33)( 24, 34)( 25, 31)( 26, 32)( 39, 41)( 40, 42)( 43, 49)( 44, 50)( 45, 47)( 46, 48)( 51, 65)( 52, 66)( 53, 63)( 54, 64)( 55, 73)( 56, 74)( 57, 71)( 58, 72)( 59, 69)( 60, 70)( 61, 67)( 62, 68)( 75, 77)( 76, 78)( 79, 85)( 80, 86)( 81, 83)( 82, 84)( 87,101)( 88,102)( 89, 99)( 90,100)( 91,109)( 92,110)( 93,107)( 94,108)( 95,105)( 96,106)( 97,103)( 98,104)(111,113)(112,114)(115,121)(116,122)(117,119)(118,120)(123,137)(124,138)(125,135)(126,136)(127,145)(128,146)(129,143)(130,144)(131,141)(132,142)(133,139)(134,140)(147,149)(148,150)(151,157)(152,158)(153,155)(154,156)(159,173)(160,174)(161,171)(162,172)(163,181)(164,182)(165,179)(166,180)(167,177)(168,178)(169,175)(170,176)(183,185)(184,186)(187,193)(188,194)(189,191)(190,192)(195,209)(196,210)(197,207)(198,208)(199,217)(200,218)(201,215)(202,216)(203,213)(204,214)(205,211)(206,212); s2 := Sym(218)!( 3, 15)( 4, 17)( 5, 16)( 6, 18)( 7, 19)( 8, 21)( 9, 20)( 10, 22)( 11, 23)( 12, 25)( 13, 24)( 14, 26)( 28, 29)( 32, 33)( 36, 37)( 39, 87)( 40, 89)( 41, 88)( 42, 90)( 43, 91)( 44, 93)( 45, 92)( 46, 94)( 47, 95)( 48, 97)( 49, 96)( 50, 98)( 51, 75)( 52, 77)( 53, 76)( 54, 78)( 55, 79)( 56, 81)( 57, 80)( 58, 82)( 59, 83)( 60, 85)( 61, 84)( 62, 86)( 63, 99)( 64,101)( 65,100)( 66,102)( 67,103)( 68,105)( 69,104)( 70,106)( 71,107)( 72,109)( 73,108)( 74,110)(111,123)(112,125)(113,124)(114,126)(115,127)(116,129)(117,128)(118,130)(119,131)(120,133)(121,132)(122,134)(136,137)(140,141)(144,145)(147,195)(148,197)(149,196)(150,198)(151,199)(152,201)(153,200)(154,202)(155,203)(156,205)(157,204)(158,206)(159,183)(160,185)(161,184)(162,186)(163,187)(164,189)(165,188)(166,190)(167,191)(168,193)(169,192)(170,194)(171,207)(172,209)(173,208)(174,210)(175,211)(176,213)(177,212)(178,214)(179,215)(180,217)(181,216)(182,218); s3 := Sym(218)!( 3,183)( 4,186)( 5,185)( 6,184)( 7,191)( 8,194)( 9,193)( 10,192)( 11,187)( 12,190)( 13,189)( 14,188)( 15,203)( 16,206)( 17,205)( 18,204)( 19,199)( 20,202)( 21,201)( 22,200)( 23,195)( 24,198)( 25,197)( 26,196)( 27,211)( 28,214)( 29,213)( 30,212)( 31,207)( 32,210)( 33,209)( 34,208)( 35,215)( 36,218)( 37,217)( 38,216)( 39,147)( 40,150)( 41,149)( 42,148)( 43,155)( 44,158)( 45,157)( 46,156)( 47,151)( 48,154)( 49,153)( 50,152)( 51,167)( 52,170)( 53,169)( 54,168)( 55,163)( 56,166)( 57,165)( 58,164)( 59,159)( 60,162)( 61,161)( 62,160)( 63,175)( 64,178)( 65,177)( 66,176)( 67,171)( 68,174)( 69,173)( 70,172)( 71,179)( 72,182)( 73,181)( 74,180)( 75,111)( 76,114)( 77,113)( 78,112)( 79,119)( 80,122)( 81,121)( 82,120)( 83,115)( 84,118)( 85,117)( 86,116)( 87,131)( 88,134)( 89,133)( 90,132)( 91,127)( 92,130)( 93,129)( 94,128)( 95,123)( 96,126)( 97,125)( 98,124)( 99,139)(100,142)(101,141)(102,140)(103,135)(104,138)(105,137)(106,136)(107,143)(108,146)(109,145)(110,144); 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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*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 >;