Overview
- Group
- SmallGroup(1728,15813)
- Rank
- 4
- Schläfli Type
- {72,6,2}
- Vertices, edges, …
- 72, 216, 6, 2
- Order of s0s1s2s3
- 72
- 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
27-fold
36-fold
54-fold
72-fold
108-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 10, 21)( 11, 20)( 12, 19)( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 37, 48)( 38, 47)( 39, 46)( 40, 54)( 41, 53)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 55, 82)( 56, 84)( 57, 83)( 58, 88)( 59, 90)( 60, 89)( 61, 85)( 62, 87)( 63, 86)( 64,102)( 65,101)( 66,100)( 67,108)( 68,107)( 69,106)( 70,105)( 71,104)( 72,103)( 73, 93)( 74, 92)( 75, 91)( 76, 99)( 77, 98)( 78, 97)( 79, 96)( 80, 95)( 81, 94)(109,163)(110,165)(111,164)(112,169)(113,171)(114,170)(115,166)(116,168)(117,167)(118,183)(119,182)(120,181)(121,189)(122,188)(123,187)(124,186)(125,185)(126,184)(127,174)(128,173)(129,172)(130,180)(131,179)(132,178)(133,177)(134,176)(135,175)(136,190)(137,192)(138,191)(139,196)(140,198)(141,197)(142,193)(143,195)(144,194)(145,210)(146,209)(147,208)(148,216)(149,215)(150,214)(151,213)(152,212)(153,211)(154,201)(155,200)(156,199)(157,207)(158,206)(159,205)(160,204)(161,203)(162,202);; s1 := ( 1,121)( 2,123)( 3,122)( 4,118)( 5,120)( 6,119)( 7,124)( 8,126)( 9,125)( 10,112)( 11,114)( 12,113)( 13,109)( 14,111)( 15,110)( 16,115)( 17,117)( 18,116)( 19,132)( 20,131)( 21,130)( 22,129)( 23,128)( 24,127)( 25,135)( 26,134)( 27,133)( 28,148)( 29,150)( 30,149)( 31,145)( 32,147)( 33,146)( 34,151)( 35,153)( 36,152)( 37,139)( 38,141)( 39,140)( 40,136)( 41,138)( 42,137)( 43,142)( 44,144)( 45,143)( 46,159)( 47,158)( 48,157)( 49,156)( 50,155)( 51,154)( 52,162)( 53,161)( 54,160)( 55,202)( 56,204)( 57,203)( 58,199)( 59,201)( 60,200)( 61,205)( 62,207)( 63,206)( 64,193)( 65,195)( 66,194)( 67,190)( 68,192)( 69,191)( 70,196)( 71,198)( 72,197)( 73,213)( 74,212)( 75,211)( 76,210)( 77,209)( 78,208)( 79,216)( 80,215)( 81,214)( 82,175)( 83,177)( 84,176)( 85,172)( 86,174)( 87,173)( 88,178)( 89,180)( 90,179)( 91,166)( 92,168)( 93,167)( 94,163)( 95,165)( 96,164)( 97,169)( 98,171)( 99,170)(100,186)(101,185)(102,184)(103,183)(104,182)(105,181)(106,189)(107,188)(108,187);; s2 := ( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)( 50, 53)( 51, 54)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(112,115)(113,116)(114,117)(121,124)(122,125)(123,126)(130,133)(131,134)(132,135)(139,142)(140,143)(141,144)(148,151)(149,152)(150,153)(157,160)(158,161)(159,162)(166,169)(167,170)(168,171)(175,178)(176,179)(177,180)(184,187)(185,188)(186,189)(193,196)(194,197)(195,198)(202,205)(203,206)(204,207)(211,214)(212,215)(213,216);; 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,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(218)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 10, 21)( 11, 20)( 12, 19)( 13, 27)( 14, 26)( 15, 25)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 37, 48)( 38, 47)( 39, 46)( 40, 54)( 41, 53)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 55, 82)( 56, 84)( 57, 83)( 58, 88)( 59, 90)( 60, 89)( 61, 85)( 62, 87)( 63, 86)( 64,102)( 65,101)( 66,100)( 67,108)( 68,107)( 69,106)( 70,105)( 71,104)( 72,103)( 73, 93)( 74, 92)( 75, 91)( 76, 99)( 77, 98)( 78, 97)( 79, 96)( 80, 95)( 81, 94)(109,163)(110,165)(111,164)(112,169)(113,171)(114,170)(115,166)(116,168)(117,167)(118,183)(119,182)(120,181)(121,189)(122,188)(123,187)(124,186)(125,185)(126,184)(127,174)(128,173)(129,172)(130,180)(131,179)(132,178)(133,177)(134,176)(135,175)(136,190)(137,192)(138,191)(139,196)(140,198)(141,197)(142,193)(143,195)(144,194)(145,210)(146,209)(147,208)(148,216)(149,215)(150,214)(151,213)(152,212)(153,211)(154,201)(155,200)(156,199)(157,207)(158,206)(159,205)(160,204)(161,203)(162,202); s1 := Sym(218)!( 1,121)( 2,123)( 3,122)( 4,118)( 5,120)( 6,119)( 7,124)( 8,126)( 9,125)( 10,112)( 11,114)( 12,113)( 13,109)( 14,111)( 15,110)( 16,115)( 17,117)( 18,116)( 19,132)( 20,131)( 21,130)( 22,129)( 23,128)( 24,127)( 25,135)( 26,134)( 27,133)( 28,148)( 29,150)( 30,149)( 31,145)( 32,147)( 33,146)( 34,151)( 35,153)( 36,152)( 37,139)( 38,141)( 39,140)( 40,136)( 41,138)( 42,137)( 43,142)( 44,144)( 45,143)( 46,159)( 47,158)( 48,157)( 49,156)( 50,155)( 51,154)( 52,162)( 53,161)( 54,160)( 55,202)( 56,204)( 57,203)( 58,199)( 59,201)( 60,200)( 61,205)( 62,207)( 63,206)( 64,193)( 65,195)( 66,194)( 67,190)( 68,192)( 69,191)( 70,196)( 71,198)( 72,197)( 73,213)( 74,212)( 75,211)( 76,210)( 77,209)( 78,208)( 79,216)( 80,215)( 81,214)( 82,175)( 83,177)( 84,176)( 85,172)( 86,174)( 87,173)( 88,178)( 89,180)( 90,179)( 91,166)( 92,168)( 93,167)( 94,163)( 95,165)( 96,164)( 97,169)( 98,171)( 99,170)(100,186)(101,185)(102,184)(103,183)(104,182)(105,181)(106,189)(107,188)(108,187); s2 := Sym(218)!( 4, 7)( 5, 8)( 6, 9)( 13, 16)( 14, 17)( 15, 18)( 22, 25)( 23, 26)( 24, 27)( 31, 34)( 32, 35)( 33, 36)( 40, 43)( 41, 44)( 42, 45)( 49, 52)( 50, 53)( 51, 54)( 58, 61)( 59, 62)( 60, 63)( 67, 70)( 68, 71)( 69, 72)( 76, 79)( 77, 80)( 78, 81)( 85, 88)( 86, 89)( 87, 90)( 94, 97)( 95, 98)( 96, 99)(103,106)(104,107)(105,108)(112,115)(113,116)(114,117)(121,124)(122,125)(123,126)(130,133)(131,134)(132,135)(139,142)(140,143)(141,144)(148,151)(149,152)(150,153)(157,160)(158,161)(159,162)(166,169)(167,170)(168,171)(175,178)(176,179)(177,180)(184,187)(185,188)(186,189)(193,196)(194,197)(195,198)(202,205)(203,206)(204,207)(211,214)(212,215)(213,216); 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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;