Overview
- Group
- SmallGroup(880,217)
- Rank
- 4
- Schläfli Type
- {22,10,2}
- Vertices, edges, …
- 22, 110, 10, 2
- Order of s0s1s2s3
- 110
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
5-fold
10-fold
11-fold
22-fold
55-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)(104,107)(105,106);; s1 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 46)( 13, 45)( 14, 55)( 15, 54)( 16, 53)( 17, 52)( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67,101)( 68,100)( 69,110)( 70,109)( 71,108)( 72,107)( 73,106)( 74,105)( 75,104)( 76,103)( 77,102)( 78, 90)( 79, 89)( 80, 99)( 81, 98)( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)( 88, 91);; s2 := ( 1, 67)( 2, 68)( 3, 69)( 4, 70)( 5, 71)( 6, 72)( 7, 73)( 8, 74)( 9, 75)( 10, 76)( 11, 77)( 12, 56)( 13, 57)( 14, 58)( 15, 59)( 16, 60)( 17, 61)( 18, 62)( 19, 63)( 20, 64)( 21, 65)( 22, 66)( 23,100)( 24,101)( 25,102)( 26,103)( 27,104)( 28,105)( 29,106)( 30,107)( 31,108)( 32,109)( 33,110)( 34, 89)( 35, 90)( 36, 91)( 37, 92)( 38, 93)( 39, 94)( 40, 95)( 41, 96)( 42, 97)( 43, 98)( 44, 99)( 45, 78)( 46, 79)( 47, 80)( 48, 81)( 49, 82)( 50, 83)( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88);; s3 := (111,112);; 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, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(112)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)(104,107)(105,106); s1 := Sym(112)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 46)( 13, 45)( 14, 55)( 15, 54)( 16, 53)( 17, 52)( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67,101)( 68,100)( 69,110)( 70,109)( 71,108)( 72,107)( 73,106)( 74,105)( 75,104)( 76,103)( 77,102)( 78, 90)( 79, 89)( 80, 99)( 81, 98)( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)( 88, 91); s2 := Sym(112)!( 1, 67)( 2, 68)( 3, 69)( 4, 70)( 5, 71)( 6, 72)( 7, 73)( 8, 74)( 9, 75)( 10, 76)( 11, 77)( 12, 56)( 13, 57)( 14, 58)( 15, 59)( 16, 60)( 17, 61)( 18, 62)( 19, 63)( 20, 64)( 21, 65)( 22, 66)( 23,100)( 24,101)( 25,102)( 26,103)( 27,104)( 28,105)( 29,106)( 30,107)( 31,108)( 32,109)( 33,110)( 34, 89)( 35, 90)( 36, 91)( 37, 92)( 38, 93)( 39, 94)( 40, 95)( 41, 96)( 42, 97)( 43, 98)( 44, 99)( 45, 78)( 46, 79)( 47, 80)( 48, 81)( 49, 82)( 50, 83)( 51, 84)( 52, 85)( 53, 86)( 54, 87)( 55, 88); s3 := Sym(112)!(111,112); poly := sub<Sym(112)|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, s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;