Overview
- Group
- SmallGroup(1728,46114)
- Rank
- 4
- Schläfli Type
- {36,6,2}
- Vertices, edges, …
- 72, 216, 12, 2
- 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
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, 3)( 2, 4)( 5, 11)( 6, 12)( 7, 9)( 8, 10)( 13, 31)( 14, 32)( 15, 29)( 16, 30)( 17, 27)( 18, 28)( 19, 25)( 20, 26)( 21, 35)( 22, 36)( 23, 33)( 24, 34)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)( 49, 67)( 50, 68)( 51, 65)( 52, 66)( 53, 63)( 54, 64)( 55, 61)( 56, 62)( 57, 71)( 58, 72)( 59, 69)( 60, 70)( 73, 75)( 74, 76)( 77, 83)( 78, 84)( 79, 81)( 80, 82)( 85,103)( 86,104)( 87,101)( 88,102)( 89, 99)( 90,100)( 91, 97)( 92, 98)( 93,107)( 94,108)( 95,105)( 96,106)(109,111)(110,112)(113,119)(114,120)(115,117)(116,118)(121,139)(122,140)(123,137)(124,138)(125,135)(126,136)(127,133)(128,134)(129,143)(130,144)(131,141)(132,142)(145,147)(146,148)(149,155)(150,156)(151,153)(152,154)(157,175)(158,176)(159,173)(160,174)(161,171)(162,172)(163,169)(164,170)(165,179)(166,180)(167,177)(168,178)(181,183)(182,184)(185,191)(186,192)(187,189)(188,190)(193,211)(194,212)(195,209)(196,210)(197,207)(198,208)(199,205)(200,206)(201,215)(202,216)(203,213)(204,214);; s1 := ( 1, 13)( 2, 15)( 3, 14)( 4, 16)( 5, 21)( 6, 23)( 7, 22)( 8, 24)( 9, 17)( 10, 19)( 11, 18)( 12, 20)( 25, 29)( 26, 31)( 27, 30)( 28, 32)( 34, 35)( 37, 85)( 38, 87)( 39, 86)( 40, 88)( 41, 93)( 42, 95)( 43, 94)( 44, 96)( 45, 89)( 46, 91)( 47, 90)( 48, 92)( 49, 73)( 50, 75)( 51, 74)( 52, 76)( 53, 81)( 54, 83)( 55, 82)( 56, 84)( 57, 77)( 58, 79)( 59, 78)( 60, 80)( 61,101)( 62,103)( 63,102)( 64,104)( 65, 97)( 66, 99)( 67, 98)( 68,100)( 69,105)( 70,107)( 71,106)( 72,108)(109,121)(110,123)(111,122)(112,124)(113,129)(114,131)(115,130)(116,132)(117,125)(118,127)(119,126)(120,128)(133,137)(134,139)(135,138)(136,140)(142,143)(145,193)(146,195)(147,194)(148,196)(149,201)(150,203)(151,202)(152,204)(153,197)(154,199)(155,198)(156,200)(157,181)(158,183)(159,182)(160,184)(161,189)(162,191)(163,190)(164,192)(165,185)(166,187)(167,186)(168,188)(169,209)(170,211)(171,210)(172,212)(173,205)(174,207)(175,206)(176,208)(177,213)(178,215)(179,214)(180,216);; s2 := ( 1,181)( 2,184)( 3,183)( 4,182)( 5,185)( 6,188)( 7,187)( 8,186)( 9,189)( 10,192)( 11,191)( 12,190)( 13,193)( 14,196)( 15,195)( 16,194)( 17,197)( 18,200)( 19,199)( 20,198)( 21,201)( 22,204)( 23,203)( 24,202)( 25,205)( 26,208)( 27,207)( 28,206)( 29,209)( 30,212)( 31,211)( 32,210)( 33,213)( 34,216)( 35,215)( 36,214)( 37,145)( 38,148)( 39,147)( 40,146)( 41,149)( 42,152)( 43,151)( 44,150)( 45,153)( 46,156)( 47,155)( 48,154)( 49,157)( 50,160)( 51,159)( 52,158)( 53,161)( 54,164)( 55,163)( 56,162)( 57,165)( 58,168)( 59,167)( 60,166)( 61,169)( 62,172)( 63,171)( 64,170)( 65,173)( 66,176)( 67,175)( 68,174)( 69,177)( 70,180)( 71,179)( 72,178)( 73,109)( 74,112)( 75,111)( 76,110)( 77,113)( 78,116)( 79,115)( 80,114)( 81,117)( 82,120)( 83,119)( 84,118)( 85,121)( 86,124)( 87,123)( 88,122)( 89,125)( 90,128)( 91,127)( 92,126)( 93,129)( 94,132)( 95,131)( 96,130)( 97,133)( 98,136)( 99,135)(100,134)(101,137)(102,140)(103,139)(104,138)(105,141)(106,144)(107,143)(108,142);; s3 := (217,218);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(218)!( 1, 3)( 2, 4)( 5, 11)( 6, 12)( 7, 9)( 8, 10)( 13, 31)( 14, 32)( 15, 29)( 16, 30)( 17, 27)( 18, 28)( 19, 25)( 20, 26)( 21, 35)( 22, 36)( 23, 33)( 24, 34)( 37, 39)( 38, 40)( 41, 47)( 42, 48)( 43, 45)( 44, 46)( 49, 67)( 50, 68)( 51, 65)( 52, 66)( 53, 63)( 54, 64)( 55, 61)( 56, 62)( 57, 71)( 58, 72)( 59, 69)( 60, 70)( 73, 75)( 74, 76)( 77, 83)( 78, 84)( 79, 81)( 80, 82)( 85,103)( 86,104)( 87,101)( 88,102)( 89, 99)( 90,100)( 91, 97)( 92, 98)( 93,107)( 94,108)( 95,105)( 96,106)(109,111)(110,112)(113,119)(114,120)(115,117)(116,118)(121,139)(122,140)(123,137)(124,138)(125,135)(126,136)(127,133)(128,134)(129,143)(130,144)(131,141)(132,142)(145,147)(146,148)(149,155)(150,156)(151,153)(152,154)(157,175)(158,176)(159,173)(160,174)(161,171)(162,172)(163,169)(164,170)(165,179)(166,180)(167,177)(168,178)(181,183)(182,184)(185,191)(186,192)(187,189)(188,190)(193,211)(194,212)(195,209)(196,210)(197,207)(198,208)(199,205)(200,206)(201,215)(202,216)(203,213)(204,214); s1 := Sym(218)!( 1, 13)( 2, 15)( 3, 14)( 4, 16)( 5, 21)( 6, 23)( 7, 22)( 8, 24)( 9, 17)( 10, 19)( 11, 18)( 12, 20)( 25, 29)( 26, 31)( 27, 30)( 28, 32)( 34, 35)( 37, 85)( 38, 87)( 39, 86)( 40, 88)( 41, 93)( 42, 95)( 43, 94)( 44, 96)( 45, 89)( 46, 91)( 47, 90)( 48, 92)( 49, 73)( 50, 75)( 51, 74)( 52, 76)( 53, 81)( 54, 83)( 55, 82)( 56, 84)( 57, 77)( 58, 79)( 59, 78)( 60, 80)( 61,101)( 62,103)( 63,102)( 64,104)( 65, 97)( 66, 99)( 67, 98)( 68,100)( 69,105)( 70,107)( 71,106)( 72,108)(109,121)(110,123)(111,122)(112,124)(113,129)(114,131)(115,130)(116,132)(117,125)(118,127)(119,126)(120,128)(133,137)(134,139)(135,138)(136,140)(142,143)(145,193)(146,195)(147,194)(148,196)(149,201)(150,203)(151,202)(152,204)(153,197)(154,199)(155,198)(156,200)(157,181)(158,183)(159,182)(160,184)(161,189)(162,191)(163,190)(164,192)(165,185)(166,187)(167,186)(168,188)(169,209)(170,211)(171,210)(172,212)(173,205)(174,207)(175,206)(176,208)(177,213)(178,215)(179,214)(180,216); s2 := Sym(218)!( 1,181)( 2,184)( 3,183)( 4,182)( 5,185)( 6,188)( 7,187)( 8,186)( 9,189)( 10,192)( 11,191)( 12,190)( 13,193)( 14,196)( 15,195)( 16,194)( 17,197)( 18,200)( 19,199)( 20,198)( 21,201)( 22,204)( 23,203)( 24,202)( 25,205)( 26,208)( 27,207)( 28,206)( 29,209)( 30,212)( 31,211)( 32,210)( 33,213)( 34,216)( 35,215)( 36,214)( 37,145)( 38,148)( 39,147)( 40,146)( 41,149)( 42,152)( 43,151)( 44,150)( 45,153)( 46,156)( 47,155)( 48,154)( 49,157)( 50,160)( 51,159)( 52,158)( 53,161)( 54,164)( 55,163)( 56,162)( 57,165)( 58,168)( 59,167)( 60,166)( 61,169)( 62,172)( 63,171)( 64,170)( 65,173)( 66,176)( 67,175)( 68,174)( 69,177)( 70,180)( 71,179)( 72,178)( 73,109)( 74,112)( 75,111)( 76,110)( 77,113)( 78,116)( 79,115)( 80,114)( 81,117)( 82,120)( 83,119)( 84,118)( 85,121)( 86,124)( 87,123)( 88,122)( 89,125)( 90,128)( 91,127)( 92,126)( 93,129)( 94,132)( 95,131)( 96,130)( 97,133)( 98,136)( 99,135)(100,134)(101,137)(102,140)(103,139)(104,138)(105,141)(106,144)(107,143)(108,142); s3 := Sym(218)!(217,218); 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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0 >;