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

Author:Annauen Joy Abellana Empaces
Topic:Geometry

Reference

https://polyhedra.tessera.li/octahedron/operations

Demonstrating how to create an Octahedron using GeoGebra 3D

https://drive.google.com/file/d/1PDpxJhSNigXC5nJnRGzLiKTPWklveadU/view?usp=sharing

Instructions in Creating an Octahedron using GeoGebra 3D

https://bit.ly/3PLHavZ

Number of faces

1. How many faces does an octahedron have?

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  • A
  • B
  • C
  • D
Check my answer (3)

Number of Triangles

2. How many triangles are there in the net of an octahedron?

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  • A
  • B
  • C
  • D
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Components of an Octahedron

3. How many edges, vertices, and face does an octahedron have?

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  • A
  • B
  • C
  • D
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Symbolic Meaning of an Octahedron

4. What does an octahedron represent as a Platonic solid?

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  • A
  • B
  • C
  • D
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Study the GeoGebra Code and Create Tetrahedron and Icosahedron Platonic Solids

Instruction
  1. Study the provided GeoGebra code carefully to understand the construction process.
  2. Use GeoGebra to create the Tetrahedron and Icosahedron Platonic solids.
  3. 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
  • B
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  • D
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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
  • B
  • C
  • D
Check my answer (3)

Components of an Icosahedron

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

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  • A
  • B
  • C
  • D
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Representation of Tetrahedron

What element is represented by the Tetrahedron in classical philosophy?

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  • A
  • B
  • C
  • D
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Representation of Icosahedron

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

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  • A
  • B
  • C
  • D
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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
  • B
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  • D
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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)?

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  • D
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