Construction of Three Dimensional Geometric Forms:
This section outlines the construction of the family of three-dimensional geometric forms. These include the set of five (Regular) Platonic solids and the (Semi-regular) Archimedean solids. The characteristics and features of these Geometric forms can be defined by specifying the following parameters that define the form.
• Apices: AP
• Edges: E
• Faces: F
• Face Angles: F.a
• Dihedral angles: D.a
• Circumsphere radius: Cs.r
• Intersphere radius: Int’ s.r
• Insphere radius: Ins. r
• Centre Angle: Ca.
• Volume given edge (E): Vol.
• Regular means that all faces, and angles and angles between faces are the same. There are only five, without admitting interpretation, and form the Family of Platonic Forms.
Three are triangulated.
• Semi-regular means that the faces which make up the solid are in themselves regular, but that there is more than one type of face. These form the Family of Archimedean Geometric Forms.
Both regular and Semi-regular figures lie with all the vertices or points in a containing sphere called the Circumsphere.
• Dihedral means between two faces.
• Insphere means the sphere touching the centre of the faces inside the solid.
• Intersphere touches the centre edges of the figure.
A detailed chart outlines the details of the above parameters against each member in the family of Platonic and Archimedean forms.
These have been presented in the following order:
1. 2D drawing of development of the form.
2. Wireframe images.
3. 3D renderings of the final form.
Materials required for Geometrical Construction of paper models:
Using the above images as reference, you are encouraged to construct three dimensional paper models to understand better the concepts in geometrical construction and their inter-relationships.
The following list of material will be necessary to make paper models:
1. Drawing board.
2. T-square (good quality, inexpensive plastic ones are available).
3. Transparent plastic set squares 30/60° and 45°, Size 20 cm and protractor.
4. Transparent plastic scale marked in cm and mm 50 cm. lengths.
5. Drawing instruments – compass large, bow compass, divider (fairly accurate, sturdy and inexpensive).
6. Wooden, drawing pencils in grades 2H, H, HB, B (from hard to soft).
7. Cartridge drawing paper for drawing exercises.
8. Bond paper for notes, exploratory exercises and paper folding exercises.
9. Ivory card and box board for 3D models.
10. Metal scale to be used as cutting edge.
11. Paper cutter with blades.
12. Razor blades for sharpening pencils.
14. Tube of adhesive for model building (FEVICOL or equivalent).
15. Drawing pins or Cello-tape.