Overview
- Group
- SmallGroup(224,77)
- Rank
- 3
- Schläfli Type
- {28,4}
- Vertices, edges, …
- 28, 56, 4
- Order of s0s1s2
- 28
- Order of s0s1s2s1
- 2
- Also known as
- {28,4|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
- Self-Petrie
Quotients maximal quotients in bold
2-fold
4-fold
7-fold
8-fold
14-fold
28-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
- {56,4}*896a
- {56,8}*896a
- {56,8}*896b
- {28,8}*896a
- {56,8}*896c
- {56,8}*896d
- {112,4}*896a
- {112,4}*896b
- {28,4}*896
- {56,4}*896b
- {28,8}*896b
- {28,16}*896a
- {28,16}*896b
5-fold
6-fold
- {28,12}*1344a
- {28,24}*1344a
- {56,12}*1344a
- {28,24}*1344b
- {56,12}*1344b
- {168,4}*1344a
- {84,4}*1344a
- {168,4}*1344b
- {84,8}*1344a
- {84,8}*1344b
7-fold
8-fold
- {56,8}*1792a
- {28,8}*1792a
- {56,8}*1792b
- {56,4}*1792a
- {56,8}*1792c
- {56,8}*1792d
- {28,16}*1792a
- {112,4}*1792a
- {28,16}*1792b
- {112,4}*1792b
- {112,8}*1792a
- {56,16}*1792a
- {112,8}*1792b
- {56,16}*1792b
- {56,16}*1792c
- {112,8}*1792c
- {112,8}*1792d
- {56,16}*1792d
- {56,16}*1792e
- {112,8}*1792e
- {112,8}*1792f
- {56,16}*1792f
- {28,32}*1792a
- {224,4}*1792a
- {28,32}*1792b
- {224,4}*1792b
- {28,4}*1792
- {56,4}*1792b
- {28,8}*1792b
- {28,8}*1792c
- {56,8}*1792e
- {56,4}*1792c
- {56,4}*1792d
- {28,8}*1792d
- {56,8}*1792f
- {56,8}*1792g
- {56,8}*1792h
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)(23,28)(24,27)(25,26)(29,43)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,50)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51);; s1 := ( 1,30)( 2,29)( 3,35)( 4,34)( 5,33)( 6,32)( 7,31)( 8,37)( 9,36)(10,42)(11,41)(12,40)(13,39)(14,38)(15,44)(16,43)(17,49)(18,48)(19,47)(20,46)(21,45)(22,51)(23,50)(24,56)(25,55)(26,54)(27,53)(28,52);; s2 := (29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56);; 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*s2*s1*s0*s1*s2*s1,
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(56)!( 2, 7)( 3, 6)( 4, 5)( 9,14)(10,13)(11,12)(16,21)(17,20)(18,19)(23,28)(24,27)(25,26)(29,43)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,50)(37,56)(38,55)(39,54)(40,53)(41,52)(42,51); s1 := Sym(56)!( 1,30)( 2,29)( 3,35)( 4,34)( 5,33)( 6,32)( 7,31)( 8,37)( 9,36)(10,42)(11,41)(12,40)(13,39)(14,38)(15,44)(16,43)(17,49)(18,48)(19,47)(20,46)(21,45)(22,51)(23,50)(24,56)(25,55)(26,54)(27,53)(28,52); s2 := Sym(56)!(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56); poly := sub<Sym(56)|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*s2*s1*s0*s1*s2*s1, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.