Overview
- Group
- SmallGroup(432,324)
- Rank
- 3
- Schläfli Type
- {12,6}
- Vertices, edges, …
- 36, 108, 18
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Self-Petrie
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
Covers minimal covers in bold
2-fold
3-fold
4-fold
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)( 51, 53)( 55, 82)( 56, 84)( 57, 83)( 58, 88)( 59, 90)( 60, 89)( 61, 85)( 62, 87)( 63, 86)( 64, 91)( 65, 93)( 66, 92)( 67, 97)( 68, 99)( 69, 98)( 70, 94)( 71, 96)( 72, 95)( 73,100)( 74,102)( 75,101)( 76,106)( 77,108)( 78,107)( 79,103)( 80,105)( 81,104);; s1 := ( 1, 58)( 2, 59)( 3, 60)( 4, 55)( 5, 56)( 6, 57)( 7, 61)( 8, 62)( 9, 63)( 10, 76)( 11, 77)( 12, 78)( 13, 73)( 14, 74)( 15, 75)( 16, 79)( 17, 80)( 18, 81)( 19, 67)( 20, 68)( 21, 69)( 22, 64)( 23, 65)( 24, 66)( 25, 70)( 26, 71)( 27, 72)( 28, 85)( 29, 86)( 30, 87)( 31, 82)( 32, 83)( 33, 84)( 34, 88)( 35, 89)( 36, 90)( 37,103)( 38,104)( 39,105)( 40,100)( 41,101)( 42,102)( 43,106)( 44,107)( 45,108)( 46, 94)( 47, 95)( 48, 96)( 49, 91)( 50, 92)( 51, 93)( 52, 97)( 53, 98)( 54, 99);; s2 := ( 1, 10)( 2, 11)( 3, 12)( 4, 18)( 5, 16)( 6, 17)( 7, 14)( 8, 15)( 9, 13)( 22, 27)( 23, 25)( 24, 26)( 28, 37)( 29, 38)( 30, 39)( 31, 45)( 32, 43)( 33, 44)( 34, 41)( 35, 42)( 36, 40)( 49, 54)( 50, 52)( 51, 53)( 55, 64)( 56, 65)( 57, 66)( 58, 72)( 59, 70)( 60, 71)( 61, 68)( 62, 69)( 63, 67)( 76, 81)( 77, 79)( 78, 80)( 82, 91)( 83, 92)( 84, 93)( 85, 99)( 86, 97)( 87, 98)( 88, 95)( 89, 96)( 90, 94)(103,108)(104,106)(105,107);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*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)( 11, 12)( 13, 16)( 14, 18)( 15, 17)( 20, 21)( 22, 25)( 23, 27)( 24, 26)( 29, 30)( 31, 34)( 32, 36)( 33, 35)( 38, 39)( 40, 43)( 41, 45)( 42, 44)( 47, 48)( 49, 52)( 50, 54)( 51, 53)( 55, 82)( 56, 84)( 57, 83)( 58, 88)( 59, 90)( 60, 89)( 61, 85)( 62, 87)( 63, 86)( 64, 91)( 65, 93)( 66, 92)( 67, 97)( 68, 99)( 69, 98)( 70, 94)( 71, 96)( 72, 95)( 73,100)( 74,102)( 75,101)( 76,106)( 77,108)( 78,107)( 79,103)( 80,105)( 81,104); s1 := Sym(108)!( 1, 58)( 2, 59)( 3, 60)( 4, 55)( 5, 56)( 6, 57)( 7, 61)( 8, 62)( 9, 63)( 10, 76)( 11, 77)( 12, 78)( 13, 73)( 14, 74)( 15, 75)( 16, 79)( 17, 80)( 18, 81)( 19, 67)( 20, 68)( 21, 69)( 22, 64)( 23, 65)( 24, 66)( 25, 70)( 26, 71)( 27, 72)( 28, 85)( 29, 86)( 30, 87)( 31, 82)( 32, 83)( 33, 84)( 34, 88)( 35, 89)( 36, 90)( 37,103)( 38,104)( 39,105)( 40,100)( 41,101)( 42,102)( 43,106)( 44,107)( 45,108)( 46, 94)( 47, 95)( 48, 96)( 49, 91)( 50, 92)( 51, 93)( 52, 97)( 53, 98)( 54, 99); s2 := Sym(108)!( 1, 10)( 2, 11)( 3, 12)( 4, 18)( 5, 16)( 6, 17)( 7, 14)( 8, 15)( 9, 13)( 22, 27)( 23, 25)( 24, 26)( 28, 37)( 29, 38)( 30, 39)( 31, 45)( 32, 43)( 33, 44)( 34, 41)( 35, 42)( 36, 40)( 49, 54)( 50, 52)( 51, 53)( 55, 64)( 56, 65)( 57, 66)( 58, 72)( 59, 70)( 60, 71)( 61, 68)( 62, 69)( 63, 67)( 76, 81)( 77, 79)( 78, 80)( 82, 91)( 83, 92)( 84, 93)( 85, 99)( 86, 97)( 87, 98)( 88, 95)( 89, 96)( 90, 94)(103,108)(104,106)(105,107); poly := sub<Sym(108)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*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.