Understanding Regular Polyhedra

Understanding Regular Polyhedra

Assessment

Interactive Video

Mathematics, Science

9th - 12th Grade

Practice Problem

Easy

Created by

Emma Peterson

Used 2+ times

FREE Resource

The video tutorial provides a proof that there are exactly five regular polyhedra, known as the Platonic solids. It explores four cases based on the type of regular polygonal faces: triangles, squares, pentagons, and n-gons with n ≥ 6. For triangular faces, the tetrahedron, octahedron, and icosahedron are identified. For square faces, only the cube is possible. For pentagonal faces, the dodecahedron is the only solution. No regular polyhedra exist with faces larger than pentagons. The proof uses Euler's formula and mathematical reasoning to determine the possible configurations.

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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a key characteristic of a regular polyhedron?

All faces are identical regular polygons.

Each vertex has a different degree.

It has an infinite number of faces.

All faces are different regular polygons.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which regular polyhedron has triangular faces and four faces in total?

Cube

Tetrahedron

Dodecahedron

Icosahedron

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many faces does an octahedron have?

12

6

4

8

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the maximum number of regular polyhedra possible with triangular faces?

One

Two

Three

Four

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the only regular polyhedron with square faces?

Icosahedron

Dodecahedron

Cube

Tetrahedron

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the context of regular polyhedra, what is the degree of each vertex in a cube?

5

3

2

4

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which regular polyhedron has pentagonal faces?

Tetrahedron

Cube

Icosahedron

Dodecahedron

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