GeometricShape

Geometric shape refers to a figure or form with defined boundaries in space. Shapes can be two-dimensional, such as polygons and curves, or three-dimensional, such as solids. In two dimensions, polygons are built from straight-line segments connected to form closed figures; common types include triangles, quadrilaterals, pentagons, and more. Regular polygons have equal sides and angles; irregular polygons do not. Circles and other conic sections—ellipse, parabola, hyperbola—are smooth curves without straight edges.

Three-dimensional shapes, or solids, have depth in addition to length and width. Common solids include polyhedra like the cube, tetrahedron, and pyramid, as well as spheres, cylinders, cones, and prisms. Properties used to describe shapes include the number of vertices, edges, and faces for polyhedra; radius, diameter, and circumference for circles; surface area and volume to quantify size.

Shapes are classified by symmetry and congruence; two shapes are congruent if one can be rigidly moved to coincide with the other. Similar shapes have the same shape but different size. Shapes are central in geometry, aiding in measurements, proofs, design, art, and computer graphics. The study of shapes also underpins spatial reasoning and various branches of mathematics, including topology and algebraic geometry.