Study the provided GeoGebra code carefully to understand the construction process.
Use GeoGebra to create the Tetrahedron and Icosahedron Platonic solids.
Observe the completed solids and analyze their structure.

Additional Task

Determine the following for each Platonic solid:

Number of triangular faces
Number of edges
Number of vertices (points)

snippet from ChatGPT

Comparing a Tetrahedron and a Triangular Pyramid

What is the difference between a Tetrahedron and a Triangular Pyramid?

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A
A. A Tetrahedron has a square base, while a Triangular Pyramid has a triangular base.
B
B. A Tetrahedron has 4 triangular faces, while a Triangular Pyramid can have any base shape.
C
C. A Tetrahedron is a specific type of Triangular Pyramid with all equilateral triangular faces, where the base is a triangle, not a square.
D
D. A Tetrahedron has 6 vertices, while a Triangular Pyramid has 4 vertices.

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Components of a Tetrahedron

2. What is the number of triangular faces, vertices, and edges for a Tetrahedron?

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A
A. 4 triangular faces, 4 vertices, 6 edges
B
B. 3 triangular faces, 4 vertices, 6 edges
C
C. 4 triangular faces, 6 vertices, 8 edges
D
D. 5 triangular faces, 5 vertices, 10 edges

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Components of an Icosahedron

What is the number of triangular faces, vertices, and edges for an Icosahedron?

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A
A. 12 triangular faces, 12 vertices, 20 edges
B
B. 20 triangular faces, 12 vertices, 30 edges
C
C. 20 triangular faces, 20 vertices, 30 edges
D
D. 20 triangular faces, 15 vertices, 25 edges

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Representation of Tetrahedron

What element is represented by the Tetrahedron in classical philosophy?

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A
A. Fire
B
B. Earth
C
C. Water
D
D. Air

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Representation of Icosahedron

5. What element is represented by the Icosahedron in classical philosophy?

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A
A. Fire
B
B. Earth
C
C. Water
D
D. Air

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Formula when relating vertices (V), edges (E), and faces (F)

Which of the following is the correct formula relating vertices (V), edges (E), and faces (F) of a convex polyhedron?

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A
A. V+E+F=2
B
B. V−E+F=1
C
C. V−E+F=2
D
D. V×E×F=2

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To calculate the number of vertices (V) of a Platonic solid, which of the following formulas can be used based on the number of faces (F)?

Plato's Octahedron (AIR) Tetrahedron (FIRE) and Icosahedron (WATER)

Reference

Demonstrating how to create an Octahedron using GeoGebra 3D

Instructions in Creating an Octahedron using GeoGebra 3D

Number of faces

Number of Triangles

Components of an Octahedron

Symbolic Meaning of an Octahedron

Study the GeoGebra Code and Create Tetrahedron and Icosahedron Platonic Solids

Comparing a Tetrahedron and a Triangular Pyramid

Components of a Tetrahedron

Components of an Icosahedron

Representation of Tetrahedron

Representation of Icosahedron

Formula when relating vertices (V), edges (E), and faces (F)

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