Overview
- Group
- SmallGroup(1728,46671)
- Rank
- 4
- Schläfli Type
- {12,4,6}
- Vertices, edges, …
- 36, 72, 36, 6
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
9-fold
12-fold
18-fold
27-fold
36-fold
54-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=<(s0*s1)^3*s2*(s1*s0)^2*s1*s2> of order 2
6 facets
- 6 of 2-fold non-regular quotient of {12,4}*288
18 vertex figures
- 18 of {4,6}*48a
P/N, where N=<(s0*s1)^4> of order 3
6 facets
- 6 of 3-fold non-regular quotient of {12,4}*288
12 vertex figures
- 12 of {4,6}*48a
P/N, where N=<(s1*s0*s1*s2)^2> of order 3
6 facets
- 6 of 3-fold non-regular quotient of {12,4}*288
12 vertex figures
- 12 of {4,6}*48a
Representations
Permutation Representation (GAP)
s0 := ( 1, 55)( 2, 57)( 3, 56)( 4, 61)( 5, 63)( 6, 62)( 7, 58)( 8, 60)( 9, 59)( 10, 64)( 11, 66)( 12, 65)( 13, 70)( 14, 72)( 15, 71)( 16, 67)( 17, 69)( 18, 68)( 19, 73)( 20, 75)( 21, 74)( 22, 79)( 23, 81)( 24, 80)( 25, 76)( 26, 78)( 27, 77)( 28, 82)( 29, 84)( 30, 83)( 31, 88)( 32, 90)( 33, 89)( 34, 85)( 35, 87)( 36, 86)( 37, 91)( 38, 93)( 39, 92)( 40, 97)( 41, 99)( 42, 98)( 43, 94)( 44, 96)( 45, 95)( 46,100)( 47,102)( 48,101)( 49,106)( 50,108)( 51,107)( 52,103)( 53,105)( 54,104);; s1 := ( 1, 2)( 4, 6)( 8, 9)( 10, 11)( 13, 15)( 17, 18)( 19, 20)( 22, 24)( 26, 27)( 28, 29)( 31, 33)( 35, 36)( 37, 38)( 40, 42)( 44, 45)( 46, 47)( 49, 51)( 53, 54)( 55, 83)( 56, 82)( 57, 84)( 58, 87)( 59, 86)( 60, 85)( 61, 88)( 62, 90)( 63, 89)( 64, 92)( 65, 91)( 66, 93)( 67, 96)( 68, 95)( 69, 94)( 70, 97)( 71, 99)( 72, 98)( 73,101)( 74,100)( 75,102)( 76,105)( 77,104)( 78,103)( 79,106)( 80,108)( 81,107);; s2 := ( 2, 8)( 3, 6)( 4, 7)( 10, 19)( 11, 26)( 12, 24)( 13, 25)( 14, 23)( 15, 21)( 16, 22)( 17, 20)( 18, 27)( 29, 35)( 30, 33)( 31, 34)( 37, 46)( 38, 53)( 39, 51)( 40, 52)( 41, 50)( 42, 48)( 43, 49)( 44, 47)( 45, 54)( 56, 62)( 57, 60)( 58, 61)( 64, 73)( 65, 80)( 66, 78)( 67, 79)( 68, 77)( 69, 75)( 70, 76)( 71, 74)( 72, 81)( 83, 89)( 84, 87)( 85, 88)( 91,100)( 92,107)( 93,105)( 94,106)( 95,104)( 96,102)( 97,103)( 98,101)( 99,108);; s3 := ( 1,10)( 2,11)( 3,12)( 4,13)( 5,14)( 6,15)( 7,16)( 8,17)( 9,18)(28,37)(29,38)(30,39)(31,40)(32,41)(33,42)(34,43)(35,44)(36,45)(55,64)(56,65)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(82,91)(83,92)(84,93)(85,94)(86,95)(87,96)(88,97)(89,98)(90,99);; 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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(108)!( 1, 55)( 2, 57)( 3, 56)( 4, 61)( 5, 63)( 6, 62)( 7, 58)( 8, 60)( 9, 59)( 10, 64)( 11, 66)( 12, 65)( 13, 70)( 14, 72)( 15, 71)( 16, 67)( 17, 69)( 18, 68)( 19, 73)( 20, 75)( 21, 74)( 22, 79)( 23, 81)( 24, 80)( 25, 76)( 26, 78)( 27, 77)( 28, 82)( 29, 84)( 30, 83)( 31, 88)( 32, 90)( 33, 89)( 34, 85)( 35, 87)( 36, 86)( 37, 91)( 38, 93)( 39, 92)( 40, 97)( 41, 99)( 42, 98)( 43, 94)( 44, 96)( 45, 95)( 46,100)( 47,102)( 48,101)( 49,106)( 50,108)( 51,107)( 52,103)( 53,105)( 54,104); s1 := Sym(108)!( 1, 2)( 4, 6)( 8, 9)( 10, 11)( 13, 15)( 17, 18)( 19, 20)( 22, 24)( 26, 27)( 28, 29)( 31, 33)( 35, 36)( 37, 38)( 40, 42)( 44, 45)( 46, 47)( 49, 51)( 53, 54)( 55, 83)( 56, 82)( 57, 84)( 58, 87)( 59, 86)( 60, 85)( 61, 88)( 62, 90)( 63, 89)( 64, 92)( 65, 91)( 66, 93)( 67, 96)( 68, 95)( 69, 94)( 70, 97)( 71, 99)( 72, 98)( 73,101)( 74,100)( 75,102)( 76,105)( 77,104)( 78,103)( 79,106)( 80,108)( 81,107); s2 := Sym(108)!( 2, 8)( 3, 6)( 4, 7)( 10, 19)( 11, 26)( 12, 24)( 13, 25)( 14, 23)( 15, 21)( 16, 22)( 17, 20)( 18, 27)( 29, 35)( 30, 33)( 31, 34)( 37, 46)( 38, 53)( 39, 51)( 40, 52)( 41, 50)( 42, 48)( 43, 49)( 44, 47)( 45, 54)( 56, 62)( 57, 60)( 58, 61)( 64, 73)( 65, 80)( 66, 78)( 67, 79)( 68, 77)( 69, 75)( 70, 76)( 71, 74)( 72, 81)( 83, 89)( 84, 87)( 85, 88)( 91,100)( 92,107)( 93,105)( 94,106)( 95,104)( 96,102)( 97,103)( 98,101)( 99,108); s3 := Sym(108)!( 1,10)( 2,11)( 3,12)( 4,13)( 5,14)( 6,15)( 7,16)( 8,17)( 9,18)(28,37)(29,38)(30,39)(31,40)(32,41)(33,42)(34,43)(35,44)(36,45)(55,64)(56,65)(57,66)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(82,91)(83,92)(84,93)(85,94)(86,95)(87,96)(88,97)(89,98)(90,99); poly := sub<Sym(108)|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, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.