Overview
- Group
- SmallGroup(896,14227)
- Rank
- 4
- Schläfli Type
- {16,14,2}
- Vertices, edges, …
- 16, 112, 14, 2
- Order of s0s1s2s3
- 112
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
7-fold
8-fold
14-fold
16-fold
28-fold
56-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := ( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 29, 43)( 30, 44)( 31, 45)( 32, 46)( 33, 47)( 34, 48)( 35, 49)( 36, 50)( 37, 51)( 38, 52)( 39, 53)( 40, 54)( 41, 55)( 42, 56)( 57, 85)( 58, 86)( 59, 87)( 60, 88)( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)( 67, 95)( 68, 96)( 69, 97)( 70, 98)( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)( 78, 99)( 79,100)( 80,101)( 81,102)( 82,103)( 83,104)( 84,105);; s1 := ( 1, 57)( 2, 63)( 3, 62)( 4, 61)( 5, 60)( 6, 59)( 7, 58)( 8, 64)( 9, 70)( 10, 69)( 11, 68)( 12, 67)( 13, 66)( 14, 65)( 15, 78)( 16, 84)( 17, 83)( 18, 82)( 19, 81)( 20, 80)( 21, 79)( 22, 71)( 23, 77)( 24, 76)( 25, 75)( 26, 74)( 27, 73)( 28, 72)( 29, 99)( 30,105)( 31,104)( 32,103)( 33,102)( 34,101)( 35,100)( 36,106)( 37,112)( 38,111)( 39,110)( 40,109)( 41,108)( 42,107)( 43, 85)( 44, 91)( 45, 90)( 46, 89)( 47, 88)( 48, 87)( 49, 86)( 50, 92)( 51, 98)( 52, 97)( 53, 96)( 54, 95)( 55, 94)( 56, 93);; s2 := ( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)( 92, 93)( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)(109,111);; s3 := (113,114);; 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*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(114)!( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 29, 43)( 30, 44)( 31, 45)( 32, 46)( 33, 47)( 34, 48)( 35, 49)( 36, 50)( 37, 51)( 38, 52)( 39, 53)( 40, 54)( 41, 55)( 42, 56)( 57, 85)( 58, 86)( 59, 87)( 60, 88)( 61, 89)( 62, 90)( 63, 91)( 64, 92)( 65, 93)( 66, 94)( 67, 95)( 68, 96)( 69, 97)( 70, 98)( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)( 78, 99)( 79,100)( 80,101)( 81,102)( 82,103)( 83,104)( 84,105); s1 := Sym(114)!( 1, 57)( 2, 63)( 3, 62)( 4, 61)( 5, 60)( 6, 59)( 7, 58)( 8, 64)( 9, 70)( 10, 69)( 11, 68)( 12, 67)( 13, 66)( 14, 65)( 15, 78)( 16, 84)( 17, 83)( 18, 82)( 19, 81)( 20, 80)( 21, 79)( 22, 71)( 23, 77)( 24, 76)( 25, 75)( 26, 74)( 27, 73)( 28, 72)( 29, 99)( 30,105)( 31,104)( 32,103)( 33,102)( 34,101)( 35,100)( 36,106)( 37,112)( 38,111)( 39,110)( 40,109)( 41,108)( 42,107)( 43, 85)( 44, 91)( 45, 90)( 46, 89)( 47, 88)( 48, 87)( 49, 86)( 50, 92)( 51, 98)( 52, 97)( 53, 96)( 54, 95)( 55, 94)( 56, 93); s2 := Sym(114)!( 1, 2)( 3, 7)( 4, 6)( 8, 9)( 10, 14)( 11, 13)( 15, 16)( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 30)( 31, 35)( 32, 34)( 36, 37)( 38, 42)( 39, 41)( 43, 44)( 45, 49)( 46, 48)( 50, 51)( 52, 56)( 53, 55)( 57, 58)( 59, 63)( 60, 62)( 64, 65)( 66, 70)( 67, 69)( 71, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 86)( 87, 91)( 88, 90)( 92, 93)( 94, 98)( 95, 97)( 99,100)(101,105)(102,104)(106,107)(108,112)(109,111); s3 := Sym(114)!(113,114); poly := sub<Sym(114)|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*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 >;