Guide - Platonic Solids

Get to know the hexahedron, also known as a cube. This shape is 1 of the 5 Platonic solids that have intrigued mathematicians, architects, and philosophers for thousands of years. This three-dimensional shape is formed by 6 squares. Learn to build this basic 3D shape as a building block for many projects and find out about how it's used in real-life examples.

### Lesson Structure

When students go through this lesson in each section, the objectives they will learn are:

* **Imagine** – Discover the hexahedron and learn about the properties of the Platonic solid.
* **Build** – Build a hexahedron cube with 6 square faces.

Teacher Notes

Overview and Objectives

Materials

#### Teachers: Preparing Your Students (15 min)

When students begin the lesson, they start in [Overview and Objectives](#overview-and-objectives), then transition to this [Preparation](#preparation) section. Presented in their view is a vocabulary list of terms and infographics illustrating concepts across STEAM domains throughout this entire lesson.

There is an extra guide for preparing student readiness for their first engagement of new terms and content knowledge. Print or distribute the guide digitally. 

* Read through the vocabulary list. (5 minutes)
* Review the Platonic Solids. Download the optional asset and share to students. (10 minutes)

#### Vocabulary (5 minutes)

This is the list of vocabulary terms used throughout the lesson. They will be in **bold** and listed throughout the different sections. Students can always revisit the vocabulary definitions with media and questions in the lesson. (5 minutes)

#### Platonic Solids (10 minutes)

Review the Platonic Solids as they are briefly referenced in this lesson. There is an **optional** guide used as a printout or can be shared online to students before they engage this lesson. Download the optional guide. (10 minutes)

Preparation

### Hexahedron

* **Platonic solids** are shapes with regular, congruent polygons as **faces**.
* There are only 5 possible **Platonic solids**: the tetrahedron, the hexahedron (cube), dodecahedron, octahedron, and icosahedron.

  * The shapes are named after the Greek philosopher, Plato, one of the many people to study these shapes.
* The hexahedron is a simple shape made by forming 6 squares into a cube.

  * Hexahedra are the only **Platonic solid** that has a square for each of its **faces**.
  * This shape has 8 **vertices**, and 12 edges.
* A hexahedron can be combined with other shapes for building or stacking.

  * Cubes are also used in gaming to construct complex structures in a digital world.
  * They also compose the shape of sugar and some sand grains.

An advantage of housing hexahedrons (cubes), is their efficient use of space, balance, symmetry, and stacking ability. With the sharp corners and low in the number of **faces**, the hexahedron becomes limited in mobility.

Imagine

Build a hexahedron (cube)

Build

References and Extra Resources

STEAM Classroom

United States

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Common Core Mathematics

CCSS.Math.Content.2.G.A.1

Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

CCSS.Math.Content.3.G.A.1

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

CCSS.Math.Content.4.G.A.2

Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

CCSS.Math.Content.5.G.B.3

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

CCSS.Math.Content.6.G.A.4

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

CCSS.Math.Content.7.G.B.6

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Intro: Hexahedron Platonic Solid

Overview and Objectives

Lesson Structure

Overview