Geometric Solids
Go to Plato's Five Regular
Polyhedra
and Archimedean Polyhedra
MATERIAL:
The Platonian regular solids (tetrahedron, hexahedron,
octahedron, dodecahedron, icosahedron)
Semiregular 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 KeplerPoinsot. 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

 KeplerPoinsot 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.

Semiregular polyhedra:
These have faces of more than one shape. Thirteen
semiregular 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
Plato's Five Regular
Polyhedra
TETRAHEDRON

HEXAHEDRON

OCTAHEDRON

DODECAHEDRON

ICOSAHEDRON

Archimedian Polyhedra
TRUNCATED TETRAHEDRON

TRUNCATED CUBE

TRUNCATED OCTAHEDRON

SNUB CUBE

TRUNCATED OCTAHEDRON

TRUNCATED ICOSAHEDRON

SMALL RHOMBICUBOCHEDRON

GREAT RHOMBECUBOCTAHEDRON

CUBOCTAHEDRON

ICOSIDODECAHEDRON

SNUB DODECAHEDRON

SMALL RHOMBICOSIDODECAHEDRON


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