Overview
- Group
- SmallGroup(1008,919)
- Rank
- 3
- Schläfli Type
- {6,28}
- Vertices, edges, …
- 18, 252, 84
- Order of s0s1s2
- 28
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
7-fold
9-fold
14-fold
18-fold
36-fold
63-fold
126-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.
Representations
Permutation Representation (GAP)
s0 := ( 1, 64)( 2, 65)( 3, 66)( 4, 67)( 5, 68)( 6, 69)( 7, 70)( 8, 78)( 9, 79)( 10, 80)( 11, 81)( 12, 82)( 13, 83)( 14, 84)( 15, 71)( 16, 72)( 17, 73)( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22,106)( 23,107)( 24,108)( 25,109)( 26,110)( 27,111)( 28,112)( 29,120)( 30,121)( 31,122)( 32,123)( 33,124)( 34,125)( 35,126)( 36,113)( 37,114)( 38,115)( 39,116)( 40,117)( 41,118)( 42,119)( 43, 85)( 44, 86)( 45, 87)( 46, 88)( 47, 89)( 48, 90)( 49, 91)( 50, 99)( 51,100)( 52,101)( 53,102)( 54,103)( 55,104)( 56,105)( 57, 92)( 58, 93)( 59, 94)( 60, 95)( 61, 96)( 62, 97)( 63, 98);; s1 := ( 1, 22)( 2, 28)( 3, 27)( 4, 26)( 5, 25)( 6, 24)( 7, 23)( 8, 29)( 9, 35)( 10, 34)( 11, 33)( 12, 32)( 13, 31)( 14, 30)( 15, 36)( 16, 42)( 17, 41)( 18, 40)( 19, 39)( 20, 38)( 21, 37)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 64, 85)( 65, 91)( 66, 90)( 67, 89)( 68, 88)( 69, 87)( 70, 86)( 71, 92)( 72, 98)( 73, 97)( 74, 96)( 75, 95)( 76, 94)( 77, 93)( 78, 99)( 79,105)( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)(107,112)(108,111)(109,110)(114,119)(115,118)(116,117)(121,126)(122,125)(123,124);; s2 := ( 1, 2)( 3, 7)( 4, 6)( 8, 44)( 9, 43)( 10, 49)( 11, 48)( 12, 47)( 13, 46)( 14, 45)( 15, 23)( 16, 22)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 29, 58)( 30, 57)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 37)( 38, 42)( 39, 41)( 50, 51)( 52, 56)( 53, 55)( 64, 65)( 66, 70)( 67, 69)( 71,107)( 72,106)( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78, 86)( 79, 85)( 80, 91)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 92,121)( 93,120)( 94,126)( 95,125)( 96,124)( 97,123)( 98,122)( 99,100)(101,105)(102,104)(113,114)(115,119)(116,118);; 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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(126)!( 1, 64)( 2, 65)( 3, 66)( 4, 67)( 5, 68)( 6, 69)( 7, 70)( 8, 78)( 9, 79)( 10, 80)( 11, 81)( 12, 82)( 13, 83)( 14, 84)( 15, 71)( 16, 72)( 17, 73)( 18, 74)( 19, 75)( 20, 76)( 21, 77)( 22,106)( 23,107)( 24,108)( 25,109)( 26,110)( 27,111)( 28,112)( 29,120)( 30,121)( 31,122)( 32,123)( 33,124)( 34,125)( 35,126)( 36,113)( 37,114)( 38,115)( 39,116)( 40,117)( 41,118)( 42,119)( 43, 85)( 44, 86)( 45, 87)( 46, 88)( 47, 89)( 48, 90)( 49, 91)( 50, 99)( 51,100)( 52,101)( 53,102)( 54,103)( 55,104)( 56,105)( 57, 92)( 58, 93)( 59, 94)( 60, 95)( 61, 96)( 62, 97)( 63, 98); s1 := Sym(126)!( 1, 22)( 2, 28)( 3, 27)( 4, 26)( 5, 25)( 6, 24)( 7, 23)( 8, 29)( 9, 35)( 10, 34)( 11, 33)( 12, 32)( 13, 31)( 14, 30)( 15, 36)( 16, 42)( 17, 41)( 18, 40)( 19, 39)( 20, 38)( 21, 37)( 44, 49)( 45, 48)( 46, 47)( 51, 56)( 52, 55)( 53, 54)( 58, 63)( 59, 62)( 60, 61)( 64, 85)( 65, 91)( 66, 90)( 67, 89)( 68, 88)( 69, 87)( 70, 86)( 71, 92)( 72, 98)( 73, 97)( 74, 96)( 75, 95)( 76, 94)( 77, 93)( 78, 99)( 79,105)( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)(107,112)(108,111)(109,110)(114,119)(115,118)(116,117)(121,126)(122,125)(123,124); s2 := Sym(126)!( 1, 2)( 3, 7)( 4, 6)( 8, 44)( 9, 43)( 10, 49)( 11, 48)( 12, 47)( 13, 46)( 14, 45)( 15, 23)( 16, 22)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 29, 58)( 30, 57)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 37)( 38, 42)( 39, 41)( 50, 51)( 52, 56)( 53, 55)( 64, 65)( 66, 70)( 67, 69)( 71,107)( 72,106)( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78, 86)( 79, 85)( 80, 91)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 92,121)( 93,120)( 94,126)( 95,125)( 96,124)( 97,123)( 98,122)( 99,100)(101,105)(102,104)(113,114)(115,119)(116,118); poly := sub<Sym(126)|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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.