Yes, the common name for an equiangular equilateral quadrilateral would be a square, a special instance of a rhombus (four sided figure with equal sides) which is a common interpretation of "diamond" in two dimensions. If by diamond you mean "kite" then no, by definition kites are not equiangular.
Its a diamond :]
A diamond, a rhombus, or a parallelogram.
A quadrilateral with four equal-length sides and opposite angles equal (but not all four) is a rhombus. That's the usual description of a diamond shape.
That is a parallelogram; it could also be called a diamond shape.
All squares have TWO SETS of opposite, parallel sides. A square is a parallelogram with 4 equal sides and 4 equal angles (right angles) of which adjacent sides are perpendicular. The related parallelogram, the rhombus, or "diamond" shape, also has 4 equal sides, but no right angles, where opposite angles are equal and adjacent angles are supplementary (sum to 180 degrees).
Its a diamond :]
A diamond, a rhombus, or a parallelogram.
Any regular shaped polygon has equal angles and equal sides
A parallelogram, rhombus, or diamond, because a square would have FOUR right angles.
A quadrilateral with four equal-length sides and opposite angles equal (but not all four) is a rhombus. That's the usual description of a diamond shape.
That is a rhombus, an equal sided parallelogram. It is diamond-shaped.
A parallelogram, rhombus, or diamond, because a square would have FOUR right angles.
It can be. A rhombus is defined as having sides of equal length and opposte sides and opposite angles are equal. Generally they are diamond shape but by definition can also be square.
That is a parallelogram; it could also be called a diamond shape.
A shape with 4 right angles and 4 equal sides is a square. ==========================
A shape where all the sides are equal and all the angles are equal. If all sides are equal but angles or not, it is equilateral. If it is vice versa, it is equiangular.
A square has 4 equal sides with opposite angles that are equal.