Overview
- Group
- SmallGroup(1728,30394)
- Rank
- 4
- Schläfli Type
- {4,12,4}
- Vertices, edges, …
- 18, 108, 108, 4
- 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
12-fold
54-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)^2> of order 2
4 facets
- 4 of 2-fold non-regular quotient of {4,12}*432a
10 vertex figures
- 8 of {12,4}*96a
- 2 of {6,4}*48a
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s2> of order 3
4 facets
- 4 of 3-fold non-regular quotient of {4,12}*432a
6 vertex figures
- 6 of {12,4}*96a
P/N, where N=<(s0*s1)^2, (s0*s1*s2*s1)^2> of order 6
4 facets
- 4 of 6-fold non-regular quotient of {4,12}*432a
4 vertex figures
- 2 of {12,4}*96a
- 2 of {6,4}*48a
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 22)( 5, 24)( 6, 23)( 7, 18)( 8, 17)( 9, 16)( 10, 19)( 11, 21)( 12, 20)( 14, 15)( 25, 27)( 29, 30)( 31, 49)( 32, 51)( 33, 50)( 34, 45)( 35, 44)( 36, 43)( 37, 46)( 38, 48)( 39, 47)( 41, 42)( 52, 54)( 56, 57)( 58, 76)( 59, 78)( 60, 77)( 61, 72)( 62, 71)( 63, 70)( 64, 73)( 65, 75)( 66, 74)( 68, 69)( 79, 81)( 83, 84)( 85,103)( 86,105)( 87,104)( 88, 99)( 89, 98)( 90, 97)( 91,100)( 92,102)( 93,101)( 95, 96)(106,108);; s1 := ( 2, 3)( 4, 5)( 7, 9)( 10, 25)( 11, 27)( 12, 26)( 13, 20)( 14, 19)( 15, 21)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 32)( 34, 36)( 37, 52)( 38, 54)( 39, 53)( 40, 47)( 41, 46)( 42, 48)( 43, 51)( 44, 50)( 45, 49)( 56, 57)( 58, 59)( 61, 63)( 64, 79)( 65, 81)( 66, 80)( 67, 74)( 68, 73)( 69, 75)( 70, 78)( 71, 77)( 72, 76)( 83, 84)( 85, 86)( 88, 90)( 91,106)( 92,108)( 93,107)( 94,101)( 95,100)( 96,102)( 97,105)( 98,104)( 99,103);; s2 := ( 1, 13)( 2, 15)( 3, 14)( 4, 21)( 5, 20)( 6, 19)( 8, 9)( 10, 23)( 11, 22)( 12, 24)( 16, 17)( 25, 27)( 28, 40)( 29, 42)( 30, 41)( 31, 48)( 32, 47)( 33, 46)( 35, 36)( 37, 50)( 38, 49)( 39, 51)( 43, 44)( 52, 54)( 55, 94)( 56, 96)( 57, 95)( 58,102)( 59,101)( 60,100)( 61, 88)( 62, 90)( 63, 89)( 64,104)( 65,103)( 66,105)( 67, 82)( 68, 84)( 69, 83)( 70, 98)( 71, 97)( 72, 99)( 73, 87)( 74, 86)( 75, 85)( 76, 92)( 77, 91)( 78, 93)( 79,108)( 80,107)( 81,106);; s3 := ( 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);; 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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(108)!( 2, 3)( 4, 22)( 5, 24)( 6, 23)( 7, 18)( 8, 17)( 9, 16)( 10, 19)( 11, 21)( 12, 20)( 14, 15)( 25, 27)( 29, 30)( 31, 49)( 32, 51)( 33, 50)( 34, 45)( 35, 44)( 36, 43)( 37, 46)( 38, 48)( 39, 47)( 41, 42)( 52, 54)( 56, 57)( 58, 76)( 59, 78)( 60, 77)( 61, 72)( 62, 71)( 63, 70)( 64, 73)( 65, 75)( 66, 74)( 68, 69)( 79, 81)( 83, 84)( 85,103)( 86,105)( 87,104)( 88, 99)( 89, 98)( 90, 97)( 91,100)( 92,102)( 93,101)( 95, 96)(106,108); s1 := Sym(108)!( 2, 3)( 4, 5)( 7, 9)( 10, 25)( 11, 27)( 12, 26)( 13, 20)( 14, 19)( 15, 21)( 16, 24)( 17, 23)( 18, 22)( 29, 30)( 31, 32)( 34, 36)( 37, 52)( 38, 54)( 39, 53)( 40, 47)( 41, 46)( 42, 48)( 43, 51)( 44, 50)( 45, 49)( 56, 57)( 58, 59)( 61, 63)( 64, 79)( 65, 81)( 66, 80)( 67, 74)( 68, 73)( 69, 75)( 70, 78)( 71, 77)( 72, 76)( 83, 84)( 85, 86)( 88, 90)( 91,106)( 92,108)( 93,107)( 94,101)( 95,100)( 96,102)( 97,105)( 98,104)( 99,103); s2 := Sym(108)!( 1, 13)( 2, 15)( 3, 14)( 4, 21)( 5, 20)( 6, 19)( 8, 9)( 10, 23)( 11, 22)( 12, 24)( 16, 17)( 25, 27)( 28, 40)( 29, 42)( 30, 41)( 31, 48)( 32, 47)( 33, 46)( 35, 36)( 37, 50)( 38, 49)( 39, 51)( 43, 44)( 52, 54)( 55, 94)( 56, 96)( 57, 95)( 58,102)( 59,101)( 60,100)( 61, 88)( 62, 90)( 63, 89)( 64,104)( 65,103)( 66,105)( 67, 82)( 68, 84)( 69, 83)( 70, 98)( 71, 97)( 72, 99)( 73, 87)( 74, 86)( 75, 85)( 76, 92)( 77, 91)( 78, 93)( 79,108)( 80,107)( 81,106); s3 := 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); 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, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.