Different Geometric form families are listed below:
Sphere forms a part of the Ellipsoidal family. It is visually the simplest form because it is perfectly symmetrical from all views. The single continuous double-curved surface which is at an equal distance from the center creates circular contours with no articulated axes. A sphere can only change in size.
Ellipsoids are also defined by one continuous double-curved surface, but the distance from the center gradually changes through elliptical curvatures. The ellipsoid can change its proportions along one, two or three axes.
A circular cylinder is symmetrical around the rotational axis and from top to bottom. The elemental parts are a simple curved surface and two flat circular surfaces that are parallel to each other.
The simple curved surface meets the two flat planes at the right angle and outlines their circular edges. The cylinder can change its general proportions through extension or contraction along its rotational axis.
It can also alter its proportions by changing the neutrally circular simple curved surface to an accentuated elliptically curved surface. The outline of the two base surfaces then changes from circular to elliptical.
The circular cone is a very dynamic volume because of the diagonal contour of the form due to the changing diameter of the curved surface. The elemental parts of the cone include one simple curved surface that wraps around the volume, one flat surface with a circular contour and one vertex point. The movement of the curved surfaces creates a circular edge on the flat base. At the top of the volume where the curved surface comes together at a single point, the vertex is created.
The simplest way to change the proportions of a cone is to extend it along its primary, rotational axis. However other proportional variations that vary the width or depth, require that the curved surface follows an elliptical curve and that the base plane of the cone changes to an elliptical plane.
Rectangular Volume/ Cube:
Cube is a special kind of rectangle. It is the simplest straight geometric volume because its elemental parts are all identical and the composition of the elements is at right angles and parallel. The six planes are all squares of equal size, which fixes the inherent proportions and allows no variations in width, depth or height. The only changes that can occur are in scale.
The rectangular volume is constructed of six parallel planes in right angle relationship to each other. Variations of proportions of a rectangular volume can occur along all three axes
A pyramid has similar features to a cone, such as the diagonal contour of the form and the vertex point at the top. The elemental parts of a pyramid are four triangular outlines and a fifth plane which is square or rectangular. The triangular planes meet at the vertex and form the sides. The square or rectangular plane forms the base. The change in proportions is determined by the rectangular proportions of the base and the height of the vertex.
A triangular prism is symmetrical between the two parallel triangular planes and out from the primary axis. The elemental parts include three rectangular or square planes that are at an acute or obtuse angle relationship to each other. The degree of the angle between the rectangular planes defines the shape of the two triangular planes. Changing the general proportions of a triangular prism by varying the distance between the two triangular end planes involves no structural changes in the angles between the elements. However, changing the proportions that vary the length of the sides of the base triangles introduces new angular relationships between the sides of the triangles and the rectangular surfaces.
Tetrahedron is the simplest 3D closed volume that can be constructed of flat planes. It is structurally the most stable form of all primary geometric forms, yet visually it emphasizes the dynamic edges and the opposing movement between the pointed corners of the form. The equilateral tetrahedron is made up of four identical equilateral triangular flat planes and has structural similarities with the cube. Proportional changes can be made by varying the angular relationship between the surfaces which directly changes the degree of each angle on the triangle as well as the length of the sides of the triangular planes.