Guide - Platonic Solids

Model the icosahedron, 1 of the 5 Platonic solids that have intrigued mathematicians, architects, and philosophers for thousands of years. Learn to build this symmetrical, 3D shape that features 20 triangular faces. Discover how the icosahedron is found in nature and ways it has been used by people.

Please note this resource was tailored for US schools and may require adjustments to suit UK schools.

🇬🇧 Teacher Notes

### Lesson Structure

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

* **Imagine** – Discover the icosahedron and learn about this Platonic solid.
* **Build** – Build a symmetrical icosahedron, a Platonic solid with 20 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

### Icosahedron

* **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 icosahedron has 20 regular, congruent triangles as its faces, and is **symmetrical**.
    * This shape has 30 edges and 12 **vertices**.
    * Each triangle on the icosahedron is an **equilateral triangle**.
    * There are 5 triangles meeting at each vertex.
    * Each interior angle of a regular triangle is 60°, so the sum of the interior angles of each vertex is 300°.
*  The icosahedron’s **symmetry** can be easily observed when rotating the shape.
    * Many mathematicians, philosophers, and architects have studied the icosahedron, as well as created many variations of this shape.
    * In nature, this shape is sometimes found in virus cells, certain atom clusters, and even minerals.
    * 3D artwork and decor may feature the icosahedron shape. This includes large art installations and sculptures, hanging lights, and paper designs.

The **vertices** of an icosahedron are the same no matter how long the edges are.

Common Core Mathematics

Florida - NGSSS

Imagine

Bend connectors and make a base of triangles for the icosahedron

Attach straws to begin closing the shape

Connect the last straws and connectors to complete the icosahedron

NGSS

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.

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.

CCSS.Math.Content.8.G.A.2

Students communicate complex ideas clearly and effectively by creating or using a variety of digital objects such as visualizations, models or simulations.

ISTE Students

1.6.c Creative Communicator

Identify and draw two-dimensional figures based on their defining attributes. Figures are limited to triangles, rectangles, squares, pentagons, hexagons and octagons.

MA.2.GR.1.1

Identify and draw quadrilaterals based on their defining attributes. Quadrilaterals include parallelograms, rhombi, rectangles, squares and trapezoids.

MA.3.GR.1.2

Informally explore angles as an attribute of two-dimensional figures. Identify and classify angles as acute, right, obtuse, straight or reflex.

MA.4.GR.1.1

Classify triangles or quadrilaterals into different categories based on shared defining attributes. Explain why a triangle or quadrilateral would or would not belong to a category.

MA.5.GR.1.1

Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles.

MA.6.GR.2.2

Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals.

MA.7.GR.1.2

Solve real-world problems involving surface area of right circular cylinders.

MA.7.GR.2.2

Solve mathematical and real-world problems involving volume of right circular cylinders.

MA.7.GR.2.3

Given a preimage and image generated by a single transformation, identify the transformation that describes the relationship.

Intro: Icosahedron Platonic Solid

Overview and Objectives

Lesson Structure

Overview