Overview
- Group
- SmallGroup(1728,47874)
- Rank
- 4
- Schläfli Type
- {6,12,6}
- Vertices, edges, …
- 6, 72, 72, 12
- Order of s0s1s2s3
- 6
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
4-fold
6-fold
8-fold
9-fold
12-fold
18-fold
24-fold
36-fold
48-fold
72-fold
108-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<s1*(s3*s2)^2*s1*(s2*s3)^2> of order 2
8 facets
- 4 of {6,6}*72c
- 4 of {6,12}*144c
6 vertex figures
- 6 of 2-fold non-regular quotient of {12,6}*288a
Representations
Permutation Representation (GAP)
s0 := ( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)( 96,104)(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)(124,136)(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)(132,140)(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)(160,172)(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)(168,176)(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)(196,208)(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)(204,212);; s1 := ( 1,127)( 2,128)( 3,125)( 4,126)( 5,123)( 6,124)( 7,121)( 8,122)( 9,131)( 10,132)( 11,129)( 12,130)( 13,115)( 14,116)( 15,113)( 16,114)( 17,111)( 18,112)( 19,109)( 20,110)( 21,119)( 22,120)( 23,117)( 24,118)( 25,139)( 26,140)( 27,137)( 28,138)( 29,135)( 30,136)( 31,133)( 32,134)( 33,143)( 34,144)( 35,141)( 36,142)( 37,163)( 38,164)( 39,161)( 40,162)( 41,159)( 42,160)( 43,157)( 44,158)( 45,167)( 46,168)( 47,165)( 48,166)( 49,151)( 50,152)( 51,149)( 52,150)( 53,147)( 54,148)( 55,145)( 56,146)( 57,155)( 58,156)( 59,153)( 60,154)( 61,175)( 62,176)( 63,173)( 64,174)( 65,171)( 66,172)( 67,169)( 68,170)( 69,179)( 70,180)( 71,177)( 72,178)( 73,199)( 74,200)( 75,197)( 76,198)( 77,195)( 78,196)( 79,193)( 80,194)( 81,203)( 82,204)( 83,201)( 84,202)( 85,187)( 86,188)( 87,185)( 88,186)( 89,183)( 90,184)( 91,181)( 92,182)( 93,191)( 94,192)( 95,189)( 96,190)( 97,211)( 98,212)( 99,209)(100,210)(101,207)(102,208)(103,205)(104,206)(105,215)(106,216)(107,213)(108,214);; s2 := ( 3, 4)( 7, 8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,105)( 58,106)( 59,108)( 60,107)( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 65, 89)( 66, 90)( 67, 92)( 68, 91)( 69, 93)( 70, 94)( 71, 96)( 72, 95)(111,112)(115,116)(119,120)(121,133)(122,134)(123,136)(124,135)(125,137)(126,138)(127,140)(128,139)(129,141)(130,142)(131,144)(132,143)(145,181)(146,182)(147,184)(148,183)(149,185)(150,186)(151,188)(152,187)(153,189)(154,190)(155,192)(156,191)(157,205)(158,206)(159,208)(160,207)(161,209)(162,210)(163,212)(164,211)(165,213)(166,214)(167,216)(168,215)(169,193)(170,194)(171,196)(172,195)(173,197)(174,198)(175,200)(176,199)(177,201)(178,202)(179,204)(180,203);; s3 := ( 1, 37)( 2, 40)( 3, 39)( 4, 38)( 5, 41)( 6, 44)( 7, 43)( 8, 42)( 9, 45)( 10, 48)( 11, 47)( 12, 46)( 13, 49)( 14, 52)( 15, 51)( 16, 50)( 17, 53)( 18, 56)( 19, 55)( 20, 54)( 21, 57)( 22, 60)( 23, 59)( 24, 58)( 25, 61)( 26, 64)( 27, 63)( 28, 62)( 29, 65)( 30, 68)( 31, 67)( 32, 66)( 33, 69)( 34, 72)( 35, 71)( 36, 70)( 74, 76)( 78, 80)( 82, 84)( 86, 88)( 90, 92)( 94, 96)( 98,100)(102,104)(106,108)(109,145)(110,148)(111,147)(112,146)(113,149)(114,152)(115,151)(116,150)(117,153)(118,156)(119,155)(120,154)(121,157)(122,160)(123,159)(124,158)(125,161)(126,164)(127,163)(128,162)(129,165)(130,168)(131,167)(132,166)(133,169)(134,172)(135,171)(136,170)(137,173)(138,176)(139,175)(140,174)(141,177)(142,180)(143,179)(144,178)(182,184)(186,188)(190,192)(194,196)(198,200)(202,204)(206,208)(210,212)(214,216);; 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*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1,
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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(216)!( 5, 9)( 6, 10)( 7, 11)( 8, 12)( 13, 25)( 14, 26)( 15, 27)( 16, 28)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 61)( 50, 62)( 51, 63)( 52, 64)( 53, 69)( 54, 70)( 55, 71)( 56, 72)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 77, 81)( 78, 82)( 79, 83)( 80, 84)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89,105)( 90,106)( 91,107)( 92,108)( 93,101)( 94,102)( 95,103)( 96,104)(113,117)(114,118)(115,119)(116,120)(121,133)(122,134)(123,135)(124,136)(125,141)(126,142)(127,143)(128,144)(129,137)(130,138)(131,139)(132,140)(149,153)(150,154)(151,155)(152,156)(157,169)(158,170)(159,171)(160,172)(161,177)(162,178)(163,179)(164,180)(165,173)(166,174)(167,175)(168,176)(185,189)(186,190)(187,191)(188,192)(193,205)(194,206)(195,207)(196,208)(197,213)(198,214)(199,215)(200,216)(201,209)(202,210)(203,211)(204,212); s1 := Sym(216)!( 1,127)( 2,128)( 3,125)( 4,126)( 5,123)( 6,124)( 7,121)( 8,122)( 9,131)( 10,132)( 11,129)( 12,130)( 13,115)( 14,116)( 15,113)( 16,114)( 17,111)( 18,112)( 19,109)( 20,110)( 21,119)( 22,120)( 23,117)( 24,118)( 25,139)( 26,140)( 27,137)( 28,138)( 29,135)( 30,136)( 31,133)( 32,134)( 33,143)( 34,144)( 35,141)( 36,142)( 37,163)( 38,164)( 39,161)( 40,162)( 41,159)( 42,160)( 43,157)( 44,158)( 45,167)( 46,168)( 47,165)( 48,166)( 49,151)( 50,152)( 51,149)( 52,150)( 53,147)( 54,148)( 55,145)( 56,146)( 57,155)( 58,156)( 59,153)( 60,154)( 61,175)( 62,176)( 63,173)( 64,174)( 65,171)( 66,172)( 67,169)( 68,170)( 69,179)( 70,180)( 71,177)( 72,178)( 73,199)( 74,200)( 75,197)( 76,198)( 77,195)( 78,196)( 79,193)( 80,194)( 81,203)( 82,204)( 83,201)( 84,202)( 85,187)( 86,188)( 87,185)( 88,186)( 89,183)( 90,184)( 91,181)( 92,182)( 93,191)( 94,192)( 95,189)( 96,190)( 97,211)( 98,212)( 99,209)(100,210)(101,207)(102,208)(103,205)(104,206)(105,215)(106,216)(107,213)(108,214); s2 := Sym(216)!( 3, 4)( 7, 8)( 11, 12)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 37, 73)( 38, 74)( 39, 76)( 40, 75)( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 81)( 46, 82)( 47, 84)( 48, 83)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,105)( 58,106)( 59,108)( 60,107)( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 65, 89)( 66, 90)( 67, 92)( 68, 91)( 69, 93)( 70, 94)( 71, 96)( 72, 95)(111,112)(115,116)(119,120)(121,133)(122,134)(123,136)(124,135)(125,137)(126,138)(127,140)(128,139)(129,141)(130,142)(131,144)(132,143)(145,181)(146,182)(147,184)(148,183)(149,185)(150,186)(151,188)(152,187)(153,189)(154,190)(155,192)(156,191)(157,205)(158,206)(159,208)(160,207)(161,209)(162,210)(163,212)(164,211)(165,213)(166,214)(167,216)(168,215)(169,193)(170,194)(171,196)(172,195)(173,197)(174,198)(175,200)(176,199)(177,201)(178,202)(179,204)(180,203); s3 := Sym(216)!( 1, 37)( 2, 40)( 3, 39)( 4, 38)( 5, 41)( 6, 44)( 7, 43)( 8, 42)( 9, 45)( 10, 48)( 11, 47)( 12, 46)( 13, 49)( 14, 52)( 15, 51)( 16, 50)( 17, 53)( 18, 56)( 19, 55)( 20, 54)( 21, 57)( 22, 60)( 23, 59)( 24, 58)( 25, 61)( 26, 64)( 27, 63)( 28, 62)( 29, 65)( 30, 68)( 31, 67)( 32, 66)( 33, 69)( 34, 72)( 35, 71)( 36, 70)( 74, 76)( 78, 80)( 82, 84)( 86, 88)( 90, 92)( 94, 96)( 98,100)(102,104)(106,108)(109,145)(110,148)(111,147)(112,146)(113,149)(114,152)(115,151)(116,150)(117,153)(118,156)(119,155)(120,154)(121,157)(122,160)(123,159)(124,158)(125,161)(126,164)(127,163)(128,162)(129,165)(130,168)(131,167)(132,166)(133,169)(134,172)(135,171)(136,170)(137,173)(138,176)(139,175)(140,174)(141,177)(142,180)(143,179)(144,178)(182,184)(186,188)(190,192)(194,196)(198,200)(202,204)(206,208)(210,212)(214,216); poly := sub<Sym(216)|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*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1, 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 >;
References
None.
to this polytope.