Overview
- Group
- SmallGroup(1728,46115)
- Rank
- 4
- Schläfli Type
- {2,12,18}
- Vertices, edges, …
- 2, 24, 216, 36
- Order of s0s1s2s3
- 18
- 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 := ( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 29)( 16, 30)( 17, 27)( 18, 28)( 19, 33)( 20, 34)( 21, 31)( 22, 32)( 23, 37)( 24, 38)( 25, 35)( 26, 36)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)( 51, 65)( 52, 66)( 53, 63)( 54, 64)( 55, 69)( 56, 70)( 57, 67)( 58, 68)( 59, 73)( 60, 74)( 61, 71)( 62, 72)( 75, 77)( 76, 78)( 79, 81)( 80, 82)( 83, 85)( 84, 86)( 87,101)( 88,102)( 89, 99)( 90,100)( 91,105)( 92,106)( 93,103)( 94,104)( 95,109)( 96,110)( 97,107)( 98,108)(111,113)(112,114)(115,117)(116,118)(119,121)(120,122)(123,137)(124,138)(125,135)(126,136)(127,141)(128,142)(129,139)(130,140)(131,145)(132,146)(133,143)(134,144)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,173)(160,174)(161,171)(162,172)(163,177)(164,178)(165,175)(166,176)(167,181)(168,182)(169,179)(170,180)(183,185)(184,186)(187,189)(188,190)(191,193)(192,194)(195,209)(196,210)(197,207)(198,208)(199,213)(200,214)(201,211)(202,212)(203,217)(204,218)(205,215)(206,216);; s2 := ( 3, 15)( 4, 17)( 5, 16)( 6, 18)( 7, 23)( 8, 25)( 9, 24)( 10, 26)( 11, 19)( 12, 21)( 13, 20)( 14, 22)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)( 39, 91)( 40, 93)( 41, 92)( 42, 94)( 43, 87)( 44, 89)( 45, 88)( 46, 90)( 47, 95)( 48, 97)( 49, 96)( 50, 98)( 51, 79)( 52, 81)( 53, 80)( 54, 82)( 55, 75)( 56, 77)( 57, 76)( 58, 78)( 59, 83)( 60, 85)( 61, 84)( 62, 86)( 63,103)( 64,105)( 65,104)( 66,106)( 67, 99)( 68,101)( 69,100)( 70,102)( 71,107)( 72,109)( 73,108)( 74,110)(111,123)(112,125)(113,124)(114,126)(115,131)(116,133)(117,132)(118,134)(119,127)(120,129)(121,128)(122,130)(136,137)(139,143)(140,145)(141,144)(142,146)(147,199)(148,201)(149,200)(150,202)(151,195)(152,197)(153,196)(154,198)(155,203)(156,205)(157,204)(158,206)(159,187)(160,189)(161,188)(162,190)(163,183)(164,185)(165,184)(166,186)(167,191)(168,193)(169,192)(170,194)(171,211)(172,213)(173,212)(174,214)(175,207)(176,209)(177,208)(178,210)(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)( 15,207)( 16,210)( 17,209)( 18,208)( 19,215)( 20,218)( 21,217)( 22,216)( 23,211)( 24,214)( 25,213)( 26,212)( 27,195)( 28,198)( 29,197)( 30,196)( 31,203)( 32,206)( 33,205)( 34,204)( 35,199)( 36,202)( 37,201)( 38,200)( 39,147)( 40,150)( 41,149)( 42,148)( 43,155)( 44,158)( 45,157)( 46,156)( 47,151)( 48,154)( 49,153)( 50,152)( 51,171)( 52,174)( 53,173)( 54,172)( 55,179)( 56,182)( 57,181)( 58,180)( 59,175)( 60,178)( 61,177)( 62,176)( 63,159)( 64,162)( 65,161)( 66,160)( 67,167)( 68,170)( 69,169)( 70,168)( 71,163)( 72,166)( 73,165)( 74,164)( 75,111)( 76,114)( 77,113)( 78,112)( 79,119)( 80,122)( 81,121)( 82,120)( 83,115)( 84,118)( 85,117)( 86,116)( 87,135)( 88,138)( 89,137)( 90,136)( 91,143)( 92,146)( 93,145)( 94,144)( 95,139)( 96,142)( 97,141)( 98,140)( 99,123)(100,126)(101,125)(102,124)(103,131)(104,134)(105,133)(106,132)(107,127)(108,130)(109,129)(110,128);; 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*s3*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2,
s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1,
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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(218)!(1,2); s1 := Sym(218)!( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 29)( 16, 30)( 17, 27)( 18, 28)( 19, 33)( 20, 34)( 21, 31)( 22, 32)( 23, 37)( 24, 38)( 25, 35)( 26, 36)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)( 51, 65)( 52, 66)( 53, 63)( 54, 64)( 55, 69)( 56, 70)( 57, 67)( 58, 68)( 59, 73)( 60, 74)( 61, 71)( 62, 72)( 75, 77)( 76, 78)( 79, 81)( 80, 82)( 83, 85)( 84, 86)( 87,101)( 88,102)( 89, 99)( 90,100)( 91,105)( 92,106)( 93,103)( 94,104)( 95,109)( 96,110)( 97,107)( 98,108)(111,113)(112,114)(115,117)(116,118)(119,121)(120,122)(123,137)(124,138)(125,135)(126,136)(127,141)(128,142)(129,139)(130,140)(131,145)(132,146)(133,143)(134,144)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,173)(160,174)(161,171)(162,172)(163,177)(164,178)(165,175)(166,176)(167,181)(168,182)(169,179)(170,180)(183,185)(184,186)(187,189)(188,190)(191,193)(192,194)(195,209)(196,210)(197,207)(198,208)(199,213)(200,214)(201,211)(202,212)(203,217)(204,218)(205,215)(206,216); s2 := Sym(218)!( 3, 15)( 4, 17)( 5, 16)( 6, 18)( 7, 23)( 8, 25)( 9, 24)( 10, 26)( 11, 19)( 12, 21)( 13, 20)( 14, 22)( 28, 29)( 31, 35)( 32, 37)( 33, 36)( 34, 38)( 39, 91)( 40, 93)( 41, 92)( 42, 94)( 43, 87)( 44, 89)( 45, 88)( 46, 90)( 47, 95)( 48, 97)( 49, 96)( 50, 98)( 51, 79)( 52, 81)( 53, 80)( 54, 82)( 55, 75)( 56, 77)( 57, 76)( 58, 78)( 59, 83)( 60, 85)( 61, 84)( 62, 86)( 63,103)( 64,105)( 65,104)( 66,106)( 67, 99)( 68,101)( 69,100)( 70,102)( 71,107)( 72,109)( 73,108)( 74,110)(111,123)(112,125)(113,124)(114,126)(115,131)(116,133)(117,132)(118,134)(119,127)(120,129)(121,128)(122,130)(136,137)(139,143)(140,145)(141,144)(142,146)(147,199)(148,201)(149,200)(150,202)(151,195)(152,197)(153,196)(154,198)(155,203)(156,205)(157,204)(158,206)(159,187)(160,189)(161,188)(162,190)(163,183)(164,185)(165,184)(166,186)(167,191)(168,193)(169,192)(170,194)(171,211)(172,213)(173,212)(174,214)(175,207)(176,209)(177,208)(178,210)(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)( 15,207)( 16,210)( 17,209)( 18,208)( 19,215)( 20,218)( 21,217)( 22,216)( 23,211)( 24,214)( 25,213)( 26,212)( 27,195)( 28,198)( 29,197)( 30,196)( 31,203)( 32,206)( 33,205)( 34,204)( 35,199)( 36,202)( 37,201)( 38,200)( 39,147)( 40,150)( 41,149)( 42,148)( 43,155)( 44,158)( 45,157)( 46,156)( 47,151)( 48,154)( 49,153)( 50,152)( 51,171)( 52,174)( 53,173)( 54,172)( 55,179)( 56,182)( 57,181)( 58,180)( 59,175)( 60,178)( 61,177)( 62,176)( 63,159)( 64,162)( 65,161)( 66,160)( 67,167)( 68,170)( 69,169)( 70,168)( 71,163)( 72,166)( 73,165)( 74,164)( 75,111)( 76,114)( 77,113)( 78,112)( 79,119)( 80,122)( 81,121)( 82,120)( 83,115)( 84,118)( 85,117)( 86,116)( 87,135)( 88,138)( 89,137)( 90,136)( 91,143)( 92,146)( 93,145)( 94,144)( 95,139)( 96,142)( 97,141)( 98,140)( 99,123)(100,126)(101,125)(102,124)(103,131)(104,134)(105,133)(106,132)(107,127)(108,130)(109,129)(110,128); 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*s3*s2*s1*s2*s3*s2*s3*s2, s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2, s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1, 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 >;