Geometry Understanding Space

Geometry Understanding Space

1. Three-Dimensional forms

   • We are surrounded by three-dimensional objects. We define a three-dimensional form as any form that has three dimensions.In many ways, three- dimensional geometry is just an extension of two-dimensional geometry; many of the same principles apply.
   • Dimensions
     • Width
     • height
     • depth

2. Polyhedra

   • Solids have properties, some of that are:
     • Volume (think of how much water it could hold). surface area (think of the area you would have to paint). how many vertices (corner points), faces and edges they have.
   • We can also connect polygons to form three-dimensional solids – these are called Polyhedra.
   • The sides of a polyhedron are called faces, the lines where faces meet are called edges, and the corners where edges meet are called vertices.
   • Example of polyhedra and not polyhedra

3. Platonic solids

   • They are the only polyhedra whose faces are all exactly the same. Every face is identical to every other face. For instance, a cube is a Platonic solid because all six of its faces are congruent squares. The same number of faces meet at each vertex. Every vertex has the same number of adjacent faces as every other vertex. For example, three equilateral triangles meet at each vertex of a tetrahedron.
   • Tetrahedron: A 4-faced polyhedron and all the faces are equilateral triangles. Hexahedron or cube: A 6-faced polyhedron and all the faces are squares. Octahedron: An 8-faced polyhedron and all the faces are equilateral triangles. Dodecahedron: A 12-faced polyhedron and all the faces are regular pentagons. Icosahedron: A 20-faced polyhedron and all the faces are equilateral triangles.

4. Non Polyhedra

   • Non-polyhedra describes any geometric solid that has any surface that is not flat, like a sphere, cone, or cylinder.

5. Form

   • Convex áreas that stand out Will be highlights.
   • Concave areas and openings will create shadows.
   • Closed Form sculpture- A Solid Mass with the focus on how the sculpture occupies space.Positive space.
   • Negative space is the activating force .Open forms interact with the environment.
   • Closed independent form. Solid material taking up space.

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