1 x Large metal tray (we found a lovely bronze coloured one)
1 x Wooden box for metal beads/spheres
180 x 8mm Metal beads/spheres (unmagnetized)
140 x 22mm Magnetic cylindrical rods all of same length (magnetized)
1 x Felt mat
1 x Smooth foam craft ball (d = 73mm)(not depicted in the photo)
1 x Small ceramic dish for counting vertices V
1 x Small ceramic dish for counting edges E
1 x Set of Constructing Polyhedrons Geometry Cards (downloadable version at The Framework Shop)
(The set includes 12 Polyhedrons to construct. Each of the 12 Polyhedrons has 3 matching cards, 1 picture card, 1 photo of the polyhedron constructed using the magnets, and 1 definition VEF card as depicted above. Also included are the two name labels to be applied to the back of the cards as control of error)
This is the activity (above) as it should be organized and placed upon the shelf. The smooth foam craft ball (not depicted) is required to build the Dodecahedron and the Pentakis Dodecahedron and this should be supplied in a basket or on a stand somewhere close by. The Geometry Cards should also be available on the shelf.
Presentation (1) – Constructing Polyhedrons using Definition Cards
- Select one Definition Card packet. (the packet should have 3 cards, 1 definition card, 1 picture card and 1 photo of the polyhedron made from the magnets) (we selected to construct the TETRAHEDRON)
- Place the card packet onto the Constructing Polyhedrons tray.
- Carry the tray over to a table and sit down.
- Move the tray up to make room on the table to look at the 3 cards.
- Remove the cards from out of the tray. (3 cards in hand)
- Place the picture card in front of the child.
- Say, “This is a TETRAHEDRON”.
- “A Tetrahedron has 4 faces”
- “I would like to show you how to construct a Tetrahedron using magnets”
- Place the Photo of the Tetrahedron, constructed using the magnets, beside the picture card.
- “This is how it should look when I’m done”
- Place the Definition card beside the Photo card.
- “This is the Definition card for the TETRAHEDRON. I am going to follow the instructions on this card”
- Pick up the 3 cards.
- Slide the tray in front of the child.
- Place only the definition card onto the right side of the felt mat.
- Place the Picture card on the table above the tray.
- Place the Photo card on the table above the tray to the right side of the Picture card.
- Pick up and discuss the Definition card. Read the names. Explain there is usually more than one way to describe a Polyhedron. The top name give us a sense of the geometry, possibly names you’ve already become familiar with. This name under the diagram is called the Polyhedron name. It tells us the number of faces a Polyhedron has. A tetrahedron has 4 faces, tetra means 4. This part under the Polyhedron name says Polygon Face. This tells us the types of Polygons used to build the Polyhedron. A tetrahedron is made using 4 triangles, it says 4 triangles. Now we have something here called the VEF number. V represents the number of Vertices, E represents the number of Edges and F represents the number of Faces. Every Polyhedron has a VEF number, this will help us to construct it. Here at the bottom of the card is the information on the Polyhedron Group and how many Polyhedrons belong to it. This information will become more interesting as we learn how to build the Polyhedrons together.
- Point to the V number on the card. Ask the child to tell you how many Vertices there are in a Tetrahedron? (A tetrahedron has 4 vertices)
- Place the card on the felt mat to the right side.
- Pull down the first ceramic dish. Introduce the dish. “This is the Vertice dish, here we will count the number of vertices”.
- Pull down the second ceramic dish. Introduce the dish. “This is the Edges dish, here we will count the number of edges”
- “Let’s begin constructing a tetrahedron”
- “How many vertices do we need?” (Look at the definition card V number) (V 4)
- Count 4 metal spheres into the Vertice dish, (1, 2, 3, 4)
- “How many edges do we need?”
- Look at the definition card E number. What does it say? (E 6)
- Count 6 metal rods into the Edges dish. (1, 2, 3, 4, 5, 6)
- Place the photo card on top of the Definition card.
- “It should look like this when I’m done”
- “First I am going to make the triangle face on the bottom”
- Build the triangle. One vertice, one edge, one vertice, one edge, one vertice one edge, and link the last edge to the first vertice creating a triangle.
- “Here is the triangular base”
- “Now I will make the point of the pyramid”
- Connect the three remaining edges, one by one, to the outside of each of the three vertices.
- Hold the last metal ball up over the centre of the triangle. “The three edges need to connect to this final vertice”
- Pull up the edges to connect with the fourth vertice to create the tetrahedron.
- Say, “This is a Tetrahedron”
- “How many faces does a tetrahedron have” (Check the definition card)
- Invite the child to read the F number from the definition card. (4)
- Count the number of faces on your construction. (1, 2, 3, 4)
- “Yes, my tetrahedron has 4 triangular faces?
- Compare the Photo card with your final construction to see if you have built it correctly, if it is the same. (Check the VEF again, and count again, is it the same?)
- Say, “Would you like to build a tetrahedron?”
In geometry, a polyhedron is a three-dimensional solid which consists of a collection of flat polygonal faces joined together to enclose a space. The word polyhedron derives from the Greek word poly meaning many, and the indo-European word hedron meaning seat. The plural of polyhedron is polyhedra or polyhedrons. For this activity we will be introducing some of the more simple polyhedrons as architectural building blocks, including all of 5 Platonic Solids, some of the innumerable Prisms and Antiprisms, some of the Johnson Solids of which there are 92 in total and 1 Catalan Solid, aka an Archimedean Dual of which there are 13 total. (See Polyhedron Groups) These examples are all convex in structure. It should be noted that we have given the commonly used name and the polyhedron name for each object as both seem to be of interest. The Polyhedron Name describes the number Polygonal Faces that make up the polyhedron surfaces, whereas the common names are also useful as they tend to reveal some of the more informal geometry known from prior experiences.
A polygon is a plane (2 dimensional, flat) figure that is bounded with straight lines. The triangles, quadrilaterals, pentagons, and hexagons are all examples that can be found in the Casa dei Bambini geometry cabinet. The polygon name characterizes the number of straight sides each shape has. For example the triangle has 3 sides, the pentagon 5, the octagon 8 and so forth. This way of denoting the plane figure 2D Polygons is continued when naming the 3D Polyhedrons. For example, the tetrahedron has 4 faces, the pentahedron 5 and so on. For the purpose of this activity we will be using only polygonal faces having all equal lengths. For example, the triangle, square and pentagonal faces are all equilateral.
A geometric shape is convex when all of the edges “point outwards”. That is no part of it curves or faces inward. If a shape is convex, a line segment drawn between any two points on the shape will always lie inside the shape.
Polyhedron Groups (aka solids)
- Prisms and Antiprisms (infinite)
- Platonic Solids (5)
- Archimedean Solids (13)
- Kepler-Poinsot Solids (4)
- Johnson Solids (92)
- Catalan Solids (13)
For the purpose of this activity we will be constructing polyhedrons belonging to 4 out of the 6 Polyhedron Groups outlined above. The Archimedean Solids are irregular and require many different sized rod lengths, and we are here requiring only one rod length. As well the Kepler-Poinsot Solids are a more complex, stellated variety and they will be reserved for more careful inspection later on using a different material.
Prisms and Antiprisms
In geometry, a prism is a polyhedron comprised of two regular and congruent polygons, one on the top and one on the bottom. These two congruent faces are connected by joining the corresponding vertices (top to bottom aligned) therefore creating a band of squares or rectangles around the sides.
An antiprism similarly consists of two copies of any chosen regular polygon, one on the top and one on the bottom. However, in this case one polygon is rotated or twisted, resulting in the vertices no longer aligning. Instead of a band of squares or rectngles, a band of triangles is formed. When the vertice spacing is adjusted evenly all of the triangles become equilateral.
There are an infinate number of these polyhedra and so they were given a group of their own called Prisms and Antiprisms.
A Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size) and regular (all angles equal and all sides equal) polygonal faces with the same number of faces meeting at each vertex. Only five solids meet this criteria, the Tetrahedron, the Cube, the Octahedron, the Dodecahedron, and the Icosohedron. These five solids are named after the ancient Greek philosopher Plato.
The Johnson Solids are convex polyhedra having regular faces and equal edge lengths, with the exception of the Platonic Solids, the Archimedean Solids, and the Prisms and Antiprisms. There are 92 Johnson Solids in all.
The Catalan Solids are duals of the 13 Archimedean Solids. A dual is created when the vertices of one correspond to the faces of the other, and the edges between the pairs of vertices of one correspond to the edges between pairs of faces of the other. Dual figures remain combinatorial or abstract and interestingly the dual of a dual is the original polyhedron.