## Geometric Solids

Go to Plato's Five Regular Polyhedra and Archimedean Polyhedra

### MATERIAL:

• The Platonian regular solids (tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron)
• Semi-regular solids (prisms - triangular, hexagonal, octagonal pyramids - hexagonal, etc).
• Regular curved solids (sphere, ellipsoid, ovoid)
• Solids with curved faces and plane faces (cylinder, cone, hemisphere)
• ### PURPOSE:

1) A study of the classification of geometric solids as a foundation
for the later study of geometry.

2) To learn the words which will be needed and which will allow the
child to express him or herself.

3) To make the child aware of solid forms in the environment and to
get the child to observe the environment with intelligence.

### PRESENTATION:

Place the five Platonian solids in the classroom together for the
children to handle. The children must be able to hold the solids
in their hands.

Later, after the children have handled the solids and are familiar
with them, introduce the terminology associated with the Platonian
solids.

Polyhedron and polyhedra (plural) means many faces.

Apex (plural: apices or apexes) - the vertex of an angle. A
solid is regular if the apices are the same.

Polyhedra have a face, edge, and apex. The Platonian solids were
first described by Plato.

There are nine regular solids: the five Platonian, pictured above, and the four polyhedra described by Kepler-Poinsot. Each face, apex and angle on each respective solid is the same.

Platonian solids:

1. Tetrahedron - 4 faces, each face an equilateral triangle
2. Hexahedron - 6 faces, each face is a square
3. Octahedron - 8 faces, each face is an equilateral triangle
4. Dodecahedron - 12 faces, each face is a pentagon (5 edges)
5. Icosahedron - 20 faces, each face is an equilateral triangle

Kepler-Poinsot solids: four star shaped regular polyhedra; three were
described by Kepler and one by Poinsot. The teacher should at least present a picture of these 4 solids to the children.

Semi-regular polyhedra: These have faces of more than one shape. Thirteen
semi-regular polyhedra were described by Archimedes. Present at least a picture of them so the children can see them.

Solids Bounded by Straight Lines:

Prisms:
The end face can be any regular polygon.
The sides are always rectangles.
Prisms are named by their end faces. For example, the triangular prism has triangles
as end faces, and the hexagonal prism has hexagons as the end faces.

Pyramids:
These have any regular polygon for a base and isosceles triangles with a common vertex as the sides.
A pyramid is named by its base (hexagonal pyramid, etc.).

Regular Curved Solids:

Sphere: all points on the surface are equidistant from the center
Ellipsoid: a form whose plane surfaces are either ellipses or circles
Ovoid: egg shaped
Torus: a rounded form on a circular base in the case of a circle, resembling a doughnut

When the children handle these, let them also roll them and watch
the path each takes.

Curved solids with plane and curved surfaces

Cylinder: a solid bounded by two parallel planes which are curved
Cone: a solid with a circular base joined by straight lines to the vertex
Hemisphere: half a sphere