There are a number of terms that are helpful in describing the work you are doing on the TGF Project. It is not essential to memorize all of them, but using them does make it easier for you to describe issues and form questions about your designs. It helps you critique the work of your fellow students and understand what they are doing.

Acute - an angle, either between lines, edges or planes, that is greater than 0º and less than 90º.
Archimedean Solids - three dimensional solid objects composed of two to three types of regular polygons where: all dihedral angles are convex and equal, all edges are identical, and all vertices are likewise identical. These can be composed of combinations of equilateral triangles, squares, pentagons, hexagons, octagons and decagons.
Concave- in the confluence of flat planes, it is an interior dihedral angle (an angle less than 180º). In relation to a non-planar volume, it is an indented surface.
Converge - as lines, edges or surfaces come towards one another.
Convex - in the confluence of flat planes, it is an exterior dihedral angle (an angle greater than 180º). In relation to a non-planar volume, it is a protruding surface.
Curvilinear - containing one or more curved lines or edges.
Dihedral Angle - the angle formed between two planes at the edge.
Diverge - as lines, edges or surfaces move away from one another.
Duals - polyhedra that share opposing traits in regard to the number of faces and vertices. A cube is a dual of an octahedron because the cube has 6 sides and 8 vertices, and an octahedron has 8 sides and 6 vertices. Dodecahedrons and icosahedrons are also duals; one has 12 sides and 20 vertices, and the other has 20 sides and 12 vertices. The tetrahedron is a dual of itself, with 4 sides and vertices. Note that duals share equal amounts of edges. The process of truncating eventually turns a form into its dual.
Edge - regarding a physical object, the sharp transition where two planes meet, or where the object ends and the space around it begins; it can also be a perceived boundary, depending upon one's visual point of view. For example, where a sphere in space meets the background - the sphere has no physical edges, just a perceived one.
Equilateral - a polygon with all edges being of equal length. The angles between edges do not have to be equal.
Form - the shape of an object; a description that includes the object's volume, surfaces and edges as a whole.
Irregular - a shape whose edge lengths and angles vary.
Line - a drawn or scribed mark longer than a point that is either straight or curved; the mark that goes between two points.
Obtuse - when an angle, either between lines, edges or planes, are at an angle more than 90º and less than 180º.
Parallel - where lines, edges or surfaces are spaced equally apart all along their dimension.
Perpendicular - where lines, edges or surfaces are at 90-degrees to one another.
Plane - it is the place where a surface lies, which can be flat or curved.
Platonic Solids - three dimensional solid objects composed of regular polygons of identical size and shape, where all edges are of equal length, all dihedral angles are convex and likewise identical , and all vertices are identical. There are only five in our universe:
- Tetrahedron - composed of four equilateral triangles and four vertices; each vertex is the confluence of three edges and three sides. It has six edges.
- Cube (Hexahedron) - composed of six regular squares and eight vertices; each vertex is the confluence of three edges and three sides. It has twelve edges.
- Octahedron - composed of eight equilateral triangles and six vertices; each vertex is the confluence of four edges and four sides. It has twelve edges.
- Dodecahedron - composed of twelve pentagons and twenty vertices; each vertex is the confluence of three edges and three sides. It has thirty edges.
- Icosahedron - composed of twenty triangles and twelve vertices; each vertex is the confluence of five edges and five sides. It has thirty edges.
Point - for purposes of this class it is a single small dot made with a pen, pencil, or sharp tip.
Polygon - poly means "many", and gon means edges. A polygon is a planar surface with many straight edges. Angles can be convex or concave. Any flat, straight-edged shape is a polygon. it can be regular or irregular.
Polyhedron (polyhedra) - poly means "many", and hedron means sides. A polyhedron is a flat-surfaced volume made from many polygons.
Regular - all edge lengths and meeting angles are equal, and can refer to a polygon or a polyhedron.
Side - the distinction between each plane of an object.
Solid - an object that contains no voids; also a hard surface as opposed to soft.
Stellate - to transform a flat plane into a volume with a new vertex; turning a polygon into its logical pyramidal polyhedron.
Surface - this is the real physical area of the outside of an object; it can be smooth or textured, flat or curved.
Truncate - to trim or cut back a vertex of a polyhedron, revealing a new polygonal surface and forming multiple new vertices.
Vertex (vertices, vertexes) - the point where all edges and corners converge.
Volume - the space within an object bounded by its planes; it is enclosed by its surfaces.