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Here you will learn about 3D shape names, including types of polyhedra (prisms, pyramids, platonic solids, irregular), nonpolyhedra (cones, cylinders, spheres, hemispheres) and compound 3D shapes.
Students will first learn about 3D shape names as part of geometry in 1 st grade. They expand their learning in 6 th grade when they find surface area of 3D shapes and solve real world problems involving 3D shapes.
3D shape names are the names of solid shapes that have 3 dimensions (height, width and depth). They can be categorized as either polyhedra, or nonpolyhedra.
The properties of 3D shapes can help you classify them and recall their names.
3D Shape \hspace{1.5cm}
Polyhedra (3D shapes with all flat polygonal faces)  Nonpolyhedra (3D shapes which have a curved surface) 

● Pyramids  ● Cones and other pyramids with 
Polyhedra are 3D shapes with flat faces, straight sides (edges), and sharp vertices.
All polyhedra can then be categorized as prisms, pyramids, platonic solids, or irregular polyhedra.
Here are some examples of polyhedra.
Prism  Pyramid  Platonic solid  Irregular polyhedron 

(Triangular prism)  (Square based  (Dodecahedron) 

Some 3D shapes can fit into more than one category. For example, a tetrahedron is one of the platonic solids, but it is also a triangular based pyramid.
Nonpolyhedra are 3D shapes that include curved surfaces. They may also have some flat faces, edges or vertices.
Here are some examples of nonpolyhedra.
Sphere  Cone  Cylinder  Conical Frustum 

Some of the most famous polyhedra are called the Platonic solids named after the Greek philosopher and Mathematician, Plato.
The platonic solids can also be referred to as regular polyhedra because their faces are regular polygons; each solid is made up of one type of regular polygon and can be inscribed inside a sphere.
In practical terms, this means that the solid can be used as a fair dice, where there is an equal chance of landing on each face.
For example,
Name  Tetrahedron  Cube  Octahedron  Dodecahedron  Icosahedron 

Picture  
Face shape  Equilateral  Square  Equilateral  Regular  Equilateral 
Number of faces  4  5  8  12  20 
Additional information  This solid  This solid  This solid 
A prism is a polyhedron that has congruent cross sections. In nonmathematical words, it is a 3D shape that can be sliced like a loaf of bread, and each slice will look like the same flat shape.
For example,
The rectangular prism below has a rectangular cross section that is the same for the entire depth of the shape.
For example,
The triangular prism below has a triangular cross section that is the same for the entire depth of the shape.
Questions involving prisms may ask you to calculate the volume, calculate the surface area, draw the net, or count the number of edges, faces, and vertices.
Geometrically, a cylinder is like a prism. The cross sections of a cylinder are congruent circles.
Faces, edges, and vertices are words to describe different parts of 3D shapes.
Face
A flat 2D shape  Edge
A straight line where  Vertex
A point where two 

The cube in the table above has \bf{6} faces, \bf{12} edges, and \bf{8} vertices.
A pyramid is a polyhedron that has a flat polygonal base shape and an apex. It has triangular side faces which slope to meet each other at the apex.
Base shape  Apex 

Regular pyramids
The base shape of a regular pyramid is a regular polygon (A 2D shape with straight equal sides).
All the lateral edges (edges leading from the base to the apex) are equal in length.
Irregular pyramids
The base shape of an irregular pyramid is an irregular polygon (A 2D shape with straight sides which vary in length).
The lateral edges may be different in length.
For all types of pyramids, the cross sectional areas are similar to each other.
For example,
Regular square based pyramid  Irregular hexagonal pyramid 

Square base  Hexagonal base 
Right pyramids
If the apex of the pyramid lies directly on top of the center of the base, the pyramid is a right pyramid.
Oblique pyramids
If the apex of the pyramid does not lie directly on top of the center of the base, the pyramid is an oblique pyramid.
This is illustrated in the diagrams below. The cross sectional areas of both right pyramids and oblique pyramids are similar to each other.
For example,
Right triangular pyramid  Oblique pentagonal pyramid 

Questions involving pyramids may ask you to calculate the volume, calculate the surface area, draw the net, or count the faces, edges, and vertices.
Cones can be described like pyramids; they have a circular base shape and an apex. Their crosssectional areas are similar circles. However, unlike pyramids, cones do not have sloping triangular side faces but instead have a curved side surface.
Cone 

If the apex of a pyramid or cone is sliced off, then the remaining shape is known as a frustum. The mathematical term for ‘slicing off an apex’ is ‘truncating.’ So a frustum can also be described as a truncated pyramid or truncated cone.
Truncated cone / conical frustum  Truncated square based pyramid 

If a 3D shape is a polyhedron (it is made up of flat polygonal faces) but it cannot be categorized as a prism, pyramid, or platonic solid, then it is an irregular polyhedron. An irregular polyhedron can have faces which are regular polygons or irregular polygons, or a combination of both.
For example,
The 3D shape below is a well recognized irregular polyhedron. This solid is made up of regular pentagons and regular hexagons and has the design of a soccer ball.
A compound solid is a 3D shape that is made up of other identifiable 3D shapes.
Examples
This compound solid is a polyhedra and is made up of a rectangular prism and a triangular prism.
This compound solid is a nonpolyhedra and is made up of a cylinder and a cone.
How does this relate to 6 th and 7 th grade math?
In order to categorize and name a 3D shape:
Use this worksheet to check your grade 6 to 8 students’ understanding of 3D shape names. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEUse this worksheet to check your grade 6 to 8 students’ understanding of 3D shape names. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEWhat 3D shape can be formed from this net?
i) A polyhedron (all flat polygonal faces) – go to step 2.
ii) A nonpolyhedron (includes a curved surface) – go to step 3.
All the 2D shapes that make up this net are polygons; they are all rectangles. The 3D shape it will form is therefore a polyhedron.
2Identify if all the faces are the same regular shape.
i) If yes, this is one of the Platonic solids (tetrahedron, cube, octahedron, dodecahedron or icosahedron).
ii) If no, continue to step 3.
The faces are not the same; they are different size rectangles.
This is not a platonic solid.
3Identify if the 3D shape is:
a) A pyramid or cone (3D shape with a base, an apex and similar crosssectional areas).
b) A prism or cylinder (3D shape with congruent crosssectional areas).
c) Neither.
Imagine the net folding up into a 3D shape.
The crosssectional areas are congruent as shown by these pink rectangles. This 3D shape is a type of prism.
4Name the shape.
For pyramids: the name of the base shape often forms the name of the 3D shape.
For prisms: the name of the crosssectional area often forms the name of the 3D shape.
i) For neither (polyhedron): This is an irregular polyhedron or a compound solid.
ii) For neither (nonpolyhedron): This is a sphere or hemisphere.
This is a rectangular prism, which is also called a cuboid.
The following 3D shape is made up of 4 equilateral triangles. What is the name of this 3D shape?
Identify if the 3D shape is:
i) A polyhedron (all flat polygonal faces) – go to step 2
ii) A nonpolyhedron (includes a curved surface) – go to step 3.
All the surfaces are flat and triangular. This 3D shape is therefore a polyhedron.
Identify if all the faces are the same regular shape:
i) If yes, this is one of the Platonic solids (tetrahedron, cube, octahedron, dodecahedron or icosahedron).
ii) If no, continue to step 3.
The faces are all equilateral triangles.
This is a Platonic solid.
This is a tetrahedron.
This can also be described as a triangular based pyramid.
What is the name of this 3D shape?
Identify if the 3D shape is:
i) A polyhedron (all flat polygonal faces) – go to step 2.
ii) A nonpolyhedron (includes a curved surface) – go to step 3.
All the surfaces are flat. All the faces are polygons; triangles and a pentagon. This 3D shape is therefore a polyhedron.
Identify if all the faces are the same regular shape:
i) If yes, this is one of the Platonic solids (tetrahedron, cube, octahedron, dodecahedron or icosahedron).
ii) If no, continue to step 3.
The faces are not the same. There are triangles and a pentagon.
This is not a Platonic solid.
Identify if the 3D shape is:
a) A pyramid or cone (3D shape with a base, an apex and similar crosssectional areas).
b) A prism or cylinder (3D shape with congruent crosssectional areas).
c) Neither.
This 3D shape has a pentagon as a base and an apex. The crosssectional areas are similar as shown by the yellow, blue and green pentagons in this diagram. This 3D shape is therefore a type of pyramid.
Name the shape.
For pyramids: the name of the base shape often forms the name of the 3D shape.
For prisms: the name of the crosssectional area often forms the name of the 3D shape.
i) For neither (polyhedron): This is an irregular polyhedron or a compound solid.
ii) For neither (nonpolyhedron): This is a sphere or hemisphere.
This is a pentagonal based pyramid.
The following 3D shape is made up of 8 equilateral triangles. What is the name of this 3D shape?
Identify if the 3D shape is:
i) A polyhedron (all flat polygonal faces) – go to step 2.
ii) A nonpolyhedron (includes a curved surface) – go to step 3.
All the surfaces are flat and triangular. This 3D shape is therefore a polyhedron.
Identify if all the faces are the same regular shape.
i) If yes, this is one of the Platonic solids (tetrahedron, cube, octahedron, dodecahedron or icosahedron).
ii) If no, continue to step 3.
The faces are all equilateral triangles.
This is a Platonic solid.
This is an octahedron.
What 3D shape can be formed from this net?
Identify if the 3D shape is:
i) A polyhedron (all flat polygonal faces) – go to step 2.
ii) A nonpolyhedron (includes a curved surface) – go to step 3.
The 2D shapes that make up this net are circles and a rectangle. Because they are not all polygons, the 3D shape this net will form will have a curved surface. It is therefore a nonpolyhedron; go to step 3.
Identify if the 3D shape is:
a) A pyramid or cone (3D shape with a base, an apex and similar crosssectional areas).
b) A prism or cylinder (3D shape with congruent crosssectional areas).
c) Neither.
Imagine the net folding up into a 3D shape. The rectangle will curl around the circumference of the circles.
The crosssectional areas are congruent as shown by these shaded circles. This 3D shape is a prism or cylinder.
Name the shape.
For pyramids: the name of the base shape often forms the name of the 3D shape.
For prisms: the name of the crosssectional area often forms the name of the 3D shape.
i) For neither (polyhedron): This is an irregular polyhedron or a compound solid.
ii) For neither (nonpolyhedron): This is a sphere or hemisphere.
This 3D shape is a cylinder.
Below is an image of a compound solid.
(a) Is this solid a type of pyramid or prism?
(b) What 3D shapes make up this compound solid?
Identify if the 3D shape is:
i) A polyhedron (all flat polygonal faces) – go to step 2.
ii) A nonpolyhedron (includes a curved surface) – go to step 3.
Some of the surfaces are flat and rectangular, there is also a curved surface. This 3D shape is therefore not a polyhedron.
Identify if the 3D shape is:
a) A pyramid or cone (3D shape with a base, an apex and similar crosssectional areas).
b) A prism or cylinder (3D shape with congruent crosssectional areas).
c) Neither.
The crosssectional areas are congruent as shown by the pink shapes, which are made from rectangle and a semicircle. This 3D shape is like a prism, but with a curved face.
Name the shape.
For pyramids: the name of the base shape often forms the name of the 3D shape.
For prisms: the name of the crosssectional area often forms the name of the 3D shape.
i) For neither (polyhedron): This is an irregular polyhedron or a compound solid.
ii) For neither (nonpolyhedron): This is a sphere or hemisphere.
This is a compound 3D shape. It is made up of rectangular prisms and a half of a cylinder.
1. Below is the net of a 3D shape.
What is the name of the 3D shape that can be formed from this net?
3D square
Cube
Cylinder
Quadrahedron
All the faces are the same regular shape; squares.
Therefore this net will form one of the five platonic solids.
A cube is made up of 6 squares.
2. Below is an image of a 3D shape.
What is the name of this 3D shape?
Hexagon
Hexagonal pyramid
Hexahedron
Hexagonal prism
This 3D shape has a base, an apex and similar crosssectional areas: it is therefore a pyramid.
The base shape is a hexagon, hence, it is a hexagonal pyramid.
3. Below is an image of a 3D shape.
What is the name of this 3D shape?
Right pyramid
Triangular pyramid
Tetrahedron
Triangular prism
This 3D shape has congruent crosssectional areas: it is therefore a prism.
The shape of the crosssection is a triangle, hence, it is a triangular prism.
4. Below is an image of a 3D shape which is made up of 12 regular pentagons.
What is the name of this 3D shape?
Dodecahedron
Pentagonal prism
Pentahedron
Icosahedron
All the faces are the same regular shape; regular pentagons.
Therefore this 3D shape is one of the five platonic solids.
A dodecahedron is made up of 12 regular pentagons.
5. Below is the net of a 3D shape.
What is the name of the 3D shape that can be formed from this net?
Irregular triangle
Rectangular based pyramid
Triangular based pyramid
Triangular prism
The triangle in the middle of the net will be the base and the other triangles will fold up and meet at an apex.
6. Below is an image of a 3D shape.
What is the name of this 3D shape?
Cylinder
Circular based pyramid
Sphere
Cone
This 3D shape has a base, an apex and similar crosssectional areas: it is therefore a pyramid or cone.
A cone can look ‘pyramidlike’ with a circular base.
The most common 3D shape names are cube, cylinder, sphere, rectangular prism, cone, and pyramid.
In elementary or primary school, children typically learn about basic 3D shapes such as cubes and cylinders. These shapes are often introduced along with their properties such as edges, faces, and vertices. Children learn to identify and describe these shapes, count their faces, edges, and vertices, and understand their basic attributes.
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