Overview
- Group
- SmallGroup(864,2282)
- Rank
- 3
- Schläfli Type
- {12,12}
- Vertices, edges, …
- 36, 216, 36
- 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
12-fold
27-fold
54-fold
108-fold
Covers minimal covers in bold
2-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, 5)( 7, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 23)( 14, 22)( 15, 24)( 16, 27)( 17, 26)( 18, 25)( 29, 30)( 31, 32)( 34, 36)( 37, 46)( 38, 48)( 39, 47)( 40, 50)( 41, 49)( 42, 51)( 43, 54)( 44, 53)( 45, 52)( 56, 57)( 58, 59)( 61, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 77)( 68, 76)( 69, 78)( 70, 81)( 71, 80)( 72, 79)( 83, 84)( 85, 86)( 88, 90)( 91,100)( 92,102)( 93,101)( 94,104)( 95,103)( 96,105)( 97,108)( 98,107)( 99,106);; s1 := ( 1, 2)( 4, 10)( 5, 12)( 6, 11)( 7, 21)( 8, 20)( 9, 19)( 14, 15)( 16, 22)( 17, 24)( 18, 23)( 25, 26)( 28, 29)( 31, 37)( 32, 39)( 33, 38)( 34, 48)( 35, 47)( 36, 46)( 41, 42)( 43, 49)( 44, 51)( 45, 50)( 52, 53)( 55, 83)( 56, 82)( 57, 84)( 58, 91)( 59, 93)( 60, 92)( 61,102)( 62,101)( 63,100)( 64, 85)( 65, 87)( 66, 86)( 67, 94)( 68, 96)( 69, 95)( 70,103)( 71,105)( 72,104)( 73, 90)( 74, 89)( 75, 88)( 76, 97)( 77, 99)( 78, 98)( 79,107)( 80,106)( 81,108);; s2 := ( 1, 62)( 2, 63)( 3, 61)( 4, 58)( 5, 59)( 6, 60)( 7, 57)( 8, 55)( 9, 56)( 10, 80)( 11, 81)( 12, 79)( 13, 76)( 14, 77)( 15, 78)( 16, 75)( 17, 73)( 18, 74)( 19, 71)( 20, 72)( 21, 70)( 22, 67)( 23, 68)( 24, 69)( 25, 66)( 26, 64)( 27, 65)( 28, 89)( 29, 90)( 30, 88)( 31, 85)( 32, 86)( 33, 87)( 34, 84)( 35, 82)( 36, 83)( 37,107)( 38,108)( 39,106)( 40,103)( 41,104)( 42,105)( 43,102)( 44,100)( 45,101)( 46, 98)( 47, 99)( 48, 97)( 49, 94)( 50, 95)( 51, 96)( 52, 93)( 53, 91)( 54, 92);; 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, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1,
s1*s0*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(108)!( 2, 3)( 4, 5)( 7, 9)( 10, 19)( 11, 21)( 12, 20)( 13, 23)( 14, 22)( 15, 24)( 16, 27)( 17, 26)( 18, 25)( 29, 30)( 31, 32)( 34, 36)( 37, 46)( 38, 48)( 39, 47)( 40, 50)( 41, 49)( 42, 51)( 43, 54)( 44, 53)( 45, 52)( 56, 57)( 58, 59)( 61, 63)( 64, 73)( 65, 75)( 66, 74)( 67, 77)( 68, 76)( 69, 78)( 70, 81)( 71, 80)( 72, 79)( 83, 84)( 85, 86)( 88, 90)( 91,100)( 92,102)( 93,101)( 94,104)( 95,103)( 96,105)( 97,108)( 98,107)( 99,106); s1 := Sym(108)!( 1, 2)( 4, 10)( 5, 12)( 6, 11)( 7, 21)( 8, 20)( 9, 19)( 14, 15)( 16, 22)( 17, 24)( 18, 23)( 25, 26)( 28, 29)( 31, 37)( 32, 39)( 33, 38)( 34, 48)( 35, 47)( 36, 46)( 41, 42)( 43, 49)( 44, 51)( 45, 50)( 52, 53)( 55, 83)( 56, 82)( 57, 84)( 58, 91)( 59, 93)( 60, 92)( 61,102)( 62,101)( 63,100)( 64, 85)( 65, 87)( 66, 86)( 67, 94)( 68, 96)( 69, 95)( 70,103)( 71,105)( 72,104)( 73, 90)( 74, 89)( 75, 88)( 76, 97)( 77, 99)( 78, 98)( 79,107)( 80,106)( 81,108); s2 := Sym(108)!( 1, 62)( 2, 63)( 3, 61)( 4, 58)( 5, 59)( 6, 60)( 7, 57)( 8, 55)( 9, 56)( 10, 80)( 11, 81)( 12, 79)( 13, 76)( 14, 77)( 15, 78)( 16, 75)( 17, 73)( 18, 74)( 19, 71)( 20, 72)( 21, 70)( 22, 67)( 23, 68)( 24, 69)( 25, 66)( 26, 64)( 27, 65)( 28, 89)( 29, 90)( 30, 88)( 31, 85)( 32, 86)( 33, 87)( 34, 84)( 35, 82)( 36, 83)( 37,107)( 38,108)( 39,106)( 40,103)( 41,104)( 42,105)( 43,102)( 44,100)( 45,101)( 46, 98)( 47, 99)( 48, 97)( 49, 94)( 50, 95)( 51, 96)( 52, 93)( 53, 91)( 54, 92); 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, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1, s1*s0*s1*s0*s1*s2*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.