Overview
- Group
- SmallGroup(1728,46671)
- Rank
- 4
- Schläfli Type
- {6,12,4}
- Vertices, edges, …
- 18, 108, 72, 4
- Order of s0s1s2s3
- 4
- 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
27-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)^3*s2*(s1*s0)^2*s1*s2> of order 2
4 facets
- 4 of 2-fold non-regular quotient of {6,12}*432h
9 vertex figures
- 9 of {12,4}*96a
P/N, where N=<(s0*s1)^3> of order 2
4 facets
- 4 of 2-fold non-regular quotient of {6,12}*432h
9 vertex figures
- 9 of {12,4}*96a
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2> of order 3
4 facets
- 4 of 3-fold non-regular quotient of {6,12}*432h
6 vertex figures
- 6 of {12,4}*96a
P/N, where N=<(s0*s1*s2*s1)^2> of order 3
4 facets
- 4 of 3-fold non-regular quotient of {6,12}*432h
6 vertex figures
- 6 of {12,4}*96a
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 10, 19)( 11, 21)( 12, 20)( 13, 25)( 14, 27)( 15, 26)( 16, 22)( 17, 24)( 18, 23)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)( 43, 49)( 44, 51)( 45, 50)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 73)( 65, 75)( 66, 74)( 67, 79)( 68, 81)( 69, 80)( 70, 76)( 71, 78)( 72, 77)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 91,100)( 92,102)( 93,101)( 94,106)( 95,108)( 96,107)( 97,103)( 98,105)( 99,104);; s1 := ( 1, 13)( 2, 11)( 3, 18)( 4, 10)( 5, 17)( 6, 15)( 7, 16)( 8, 14)( 9, 12)( 19, 22)( 21, 27)( 23, 26)( 28, 40)( 29, 38)( 30, 45)( 31, 37)( 32, 44)( 33, 42)( 34, 43)( 35, 41)( 36, 39)( 46, 49)( 48, 54)( 50, 53)( 55, 67)( 56, 65)( 57, 72)( 58, 64)( 59, 71)( 60, 69)( 61, 70)( 62, 68)( 63, 66)( 73, 76)( 75, 81)( 77, 80)( 82, 94)( 83, 92)( 84, 99)( 85, 91)( 86, 98)( 87, 96)( 88, 97)( 89, 95)( 90, 93)(100,103)(102,108)(104,107);; 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)( 55, 82)( 56, 83)( 57, 84)( 58, 90)( 59, 88)( 60, 89)( 61, 86)( 62, 87)( 63, 85)( 64,100)( 65,101)( 66,102)( 67,108)( 68,106)( 69,107)( 70,104)( 71,105)( 72,103)( 73, 91)( 74, 92)( 75, 93)( 76, 99)( 77, 97)( 78, 98)( 79, 95)( 80, 96)( 81, 94);; 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, 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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(108)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 10, 19)( 11, 21)( 12, 20)( 13, 25)( 14, 27)( 15, 26)( 16, 22)( 17, 24)( 18, 23)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 37, 46)( 38, 48)( 39, 47)( 40, 52)( 41, 54)( 42, 53)( 43, 49)( 44, 51)( 45, 50)( 56, 57)( 58, 61)( 59, 63)( 60, 62)( 64, 73)( 65, 75)( 66, 74)( 67, 79)( 68, 81)( 69, 80)( 70, 76)( 71, 78)( 72, 77)( 83, 84)( 85, 88)( 86, 90)( 87, 89)( 91,100)( 92,102)( 93,101)( 94,106)( 95,108)( 96,107)( 97,103)( 98,105)( 99,104); s1 := Sym(108)!( 1, 13)( 2, 11)( 3, 18)( 4, 10)( 5, 17)( 6, 15)( 7, 16)( 8, 14)( 9, 12)( 19, 22)( 21, 27)( 23, 26)( 28, 40)( 29, 38)( 30, 45)( 31, 37)( 32, 44)( 33, 42)( 34, 43)( 35, 41)( 36, 39)( 46, 49)( 48, 54)( 50, 53)( 55, 67)( 56, 65)( 57, 72)( 58, 64)( 59, 71)( 60, 69)( 61, 70)( 62, 68)( 63, 66)( 73, 76)( 75, 81)( 77, 80)( 82, 94)( 83, 92)( 84, 99)( 85, 91)( 86, 98)( 87, 96)( 88, 97)( 89, 95)( 90, 93)(100,103)(102,108)(104,107); 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)( 55, 82)( 56, 83)( 57, 84)( 58, 90)( 59, 88)( 60, 89)( 61, 86)( 62, 87)( 63, 85)( 64,100)( 65,101)( 66,102)( 67,108)( 68,106)( 69,107)( 70,104)( 71,105)( 72,103)( 73, 91)( 74, 92)( 75, 93)( 76, 99)( 77, 97)( 78, 98)( 79, 95)( 80, 96)( 81, 94); 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, 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.