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