Overview
- Group
- SmallGroup(1728,46674)
- Rank
- 4
- Schläfli Type
- {4,4,12}
- Vertices, edges, …
- 4, 36, 108, 54
- 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
6-fold
12-fold
18-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=<(s1*s2)^2> of order 2
30 facets
4 vertex figures
- 4 of 2-fold non-regular quotient of {4,12}*432b
P/N, where N=<(s1*s2*s3*s2)^2> of order 3
18 facets
- 18 of {4,4}*32
4 vertex figures
- 4 of 3-fold non-regular quotient of {4,12}*432b
P/N, where N=<s1*s2*s3*s2*s1*(s3*s2)^2*s3> of order 3
18 facets
- 18 of {4,4}*32
4 vertex figures
- 4 of 3-fold non-regular quotient of {4,12}*432b
P/N, where N=<(s1*s2)^2, (s1*s2*s3*s2)^2> of order 6
12 facets
4 vertex figures
- 4 of 6-fold non-regular quotient of {4,12}*432b
Representations
Permutation Representation (GAP)
s0 := ( 1, 55)( 2, 56)( 3, 57)( 4, 58)( 5, 59)( 6, 60)( 7, 61)( 8, 62)( 9, 63)( 10, 64)( 11, 65)( 12, 66)( 13, 67)( 14, 68)( 15, 69)( 16, 70)( 17, 71)( 18, 72)( 19, 73)( 20, 74)( 21, 75)( 22, 76)( 23, 77)( 24, 78)( 25, 79)( 26, 80)( 27, 81)( 28, 82)( 29, 83)( 30, 84)( 31, 85)( 32, 86)( 33, 87)( 34, 88)( 35, 89)( 36, 90)( 37, 91)( 38, 92)( 39, 93)( 40, 94)( 41, 95)( 42, 96)( 43, 97)( 44, 98)( 45, 99)( 46,100)( 47,101)( 48,102)( 49,103)( 50,104)( 51,105)( 52,106)( 53,107)( 54,108);; s1 := ( 2, 8)( 3, 6)( 4, 7)( 11, 17)( 12, 15)( 13, 16)( 20, 26)( 21, 24)( 22, 25)( 29, 35)( 30, 33)( 31, 34)( 38, 44)( 39, 42)( 40, 43)( 47, 53)( 48, 51)( 49, 52)( 55, 82)( 56, 89)( 57, 87)( 58, 88)( 59, 86)( 60, 84)( 61, 85)( 62, 83)( 63, 90)( 64, 91)( 65, 98)( 66, 96)( 67, 97)( 68, 95)( 69, 93)( 70, 94)( 71, 92)( 72, 99)( 73,100)( 74,107)( 75,105)( 76,106)( 77,104)( 78,102)( 79,103)( 80,101)( 81,108);; s2 := ( 4, 9)( 5, 7)( 6, 8)( 10, 19)( 11, 20)( 12, 21)( 13, 27)( 14, 25)( 15, 26)( 16, 23)( 17, 24)( 18, 22)( 31, 36)( 32, 34)( 33, 35)( 37, 46)( 38, 47)( 39, 48)( 40, 54)( 41, 52)( 42, 53)( 43, 50)( 44, 51)( 45, 49)( 58, 63)( 59, 61)( 60, 62)( 64, 73)( 65, 74)( 66, 75)( 67, 81)( 68, 79)( 69, 80)( 70, 77)( 71, 78)( 72, 76)( 85, 90)( 86, 88)( 87, 89)( 91,100)( 92,101)( 93,102)( 94,108)( 95,106)( 96,107)( 97,104)( 98,105)( 99,103);; s3 := ( 1, 14)( 2, 16)( 3, 12)( 4, 17)( 5, 10)( 6, 15)( 7, 11)( 8, 13)( 9, 18)( 19, 23)( 20, 25)( 22, 26)( 28, 41)( 29, 43)( 30, 39)( 31, 44)( 32, 37)( 33, 42)( 34, 38)( 35, 40)( 36, 45)( 46, 50)( 47, 52)( 49, 53)( 55, 68)( 56, 70)( 57, 66)( 58, 71)( 59, 64)( 60, 69)( 61, 65)( 62, 67)( 63, 72)( 73, 77)( 74, 79)( 76, 80)( 82, 95)( 83, 97)( 84, 93)( 85, 98)( 86, 91)( 87, 96)( 88, 92)( 89, 94)( 90, 99)(100,104)(101,106)(103,107);; 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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(108)!( 1, 55)( 2, 56)( 3, 57)( 4, 58)( 5, 59)( 6, 60)( 7, 61)( 8, 62)( 9, 63)( 10, 64)( 11, 65)( 12, 66)( 13, 67)( 14, 68)( 15, 69)( 16, 70)( 17, 71)( 18, 72)( 19, 73)( 20, 74)( 21, 75)( 22, 76)( 23, 77)( 24, 78)( 25, 79)( 26, 80)( 27, 81)( 28, 82)( 29, 83)( 30, 84)( 31, 85)( 32, 86)( 33, 87)( 34, 88)( 35, 89)( 36, 90)( 37, 91)( 38, 92)( 39, 93)( 40, 94)( 41, 95)( 42, 96)( 43, 97)( 44, 98)( 45, 99)( 46,100)( 47,101)( 48,102)( 49,103)( 50,104)( 51,105)( 52,106)( 53,107)( 54,108); s1 := Sym(108)!( 2, 8)( 3, 6)( 4, 7)( 11, 17)( 12, 15)( 13, 16)( 20, 26)( 21, 24)( 22, 25)( 29, 35)( 30, 33)( 31, 34)( 38, 44)( 39, 42)( 40, 43)( 47, 53)( 48, 51)( 49, 52)( 55, 82)( 56, 89)( 57, 87)( 58, 88)( 59, 86)( 60, 84)( 61, 85)( 62, 83)( 63, 90)( 64, 91)( 65, 98)( 66, 96)( 67, 97)( 68, 95)( 69, 93)( 70, 94)( 71, 92)( 72, 99)( 73,100)( 74,107)( 75,105)( 76,106)( 77,104)( 78,102)( 79,103)( 80,101)( 81,108); s2 := Sym(108)!( 4, 9)( 5, 7)( 6, 8)( 10, 19)( 11, 20)( 12, 21)( 13, 27)( 14, 25)( 15, 26)( 16, 23)( 17, 24)( 18, 22)( 31, 36)( 32, 34)( 33, 35)( 37, 46)( 38, 47)( 39, 48)( 40, 54)( 41, 52)( 42, 53)( 43, 50)( 44, 51)( 45, 49)( 58, 63)( 59, 61)( 60, 62)( 64, 73)( 65, 74)( 66, 75)( 67, 81)( 68, 79)( 69, 80)( 70, 77)( 71, 78)( 72, 76)( 85, 90)( 86, 88)( 87, 89)( 91,100)( 92,101)( 93,102)( 94,108)( 95,106)( 96,107)( 97,104)( 98,105)( 99,103); s3 := Sym(108)!( 1, 14)( 2, 16)( 3, 12)( 4, 17)( 5, 10)( 6, 15)( 7, 11)( 8, 13)( 9, 18)( 19, 23)( 20, 25)( 22, 26)( 28, 41)( 29, 43)( 30, 39)( 31, 44)( 32, 37)( 33, 42)( 34, 38)( 35, 40)( 36, 45)( 46, 50)( 47, 52)( 49, 53)( 55, 68)( 56, 70)( 57, 66)( 58, 71)( 59, 64)( 60, 69)( 61, 65)( 62, 67)( 63, 72)( 73, 77)( 74, 79)( 76, 80)( 82, 95)( 83, 97)( 84, 93)( 85, 98)( 86, 91)( 87, 96)( 88, 92)( 89, 94)( 90, 99)(100,104)(101,106)(103,107); 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, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;
References
None.
to this polytope.