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