Rhombus is a quadrilateral with equal sides and opposite parallel sides. Opposite angles are equal and diagonals bisect each other at right angles. All squares are rhombuses, but not all rhombuses are squares. Rhombus exhibits symmetry across its diagonals
Hexagon is a 2D figure with six straight edges. Named after "hex" (six) and "gonia" (corners). Can be regular or irregular based on side lengths
Angle is the space between two rays with the same endpoint. A full circle measures 360 degrees. Polygons have the same number of sides as interior angles
Degeneracy refers to limiting cases that appear simpler than the rest of a class. Many object definitions include implicit inequalities that become equalities. Degeneracy often corresponds to singularities in objects or configuration spaces
Two objects are similar if they have the same shape or can be transformed into each other. Similar shapes can be obtained by uniform scaling with translation, rotation, and reflection. All circles, squares, and equilateral triangles are similar. Ellipses, rectangles, and isosceles triangles are not all similar
Regular polygons are equiangular and equilateral, either convex or star. All vertices lie on a common circle and have a tangent incircle. Regular polygons have rotational symmetry of order n. The symmetry group is dihedral group Dn (order 2n)