Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
gptkb:symmetry |
| gptkbp:actsOn |
regular n-gon
|
| gptkbp:contains |
cyclic subgroup of order n
n reflections n rotations |
| gptkbp:first_studied_in |
19th century
|
| gptkbp:generation |
rotation and reflection
|
| gptkbp:has_elements |
reflections
rotations |
| gptkbp:has_identity_element |
rotation by 0 degrees
|
| gptkbp:has_order_2_elements |
reflections
|
| gptkbp:hasSubgroup |
gptkb:symmetric_group_S_n
|
| https://www.w3.org/2000/01/rdf-schema#label |
Dihedral group
|
| gptkbp:is_abelian |
for n = 1 or 2
|
| gptkbp:is_not_simple |
for n > 2
|
| gptkbp:is_solvable |
for all n
|
| gptkbp:isNonAbelian |
for n > 2
|
| gptkbp:isomorphicTo |
symmetry group of regular polygon
|
| gptkbp:isSimple |
for n = 2
|
| gptkbp:namedFor |
gptkb:Arthur_Cayley
|
| gptkbp:notation |
D_n
Dih_n |
| gptkbp:order |
2n
|
| gptkbp:order_of_D_3 |
6
|
| gptkbp:order_of_D_4 |
8
|
| gptkbp:presentedBy |
< r, s | r^n = s^2 = 1, s r s^{-1} = r^{-1} >
|
| gptkbp:used_in |
gptkb:geometry
crystallography group theory |
| gptkbp:bfsParent |
gptkb:Triangle_Group
|
| gptkbp:bfsLayer |
5
|