3-D Solids: Faces, Edges and Vertices

by Laurie Laurendeau on February 28, 2012

A 3-D solid (sometimes called a 3-D shape) is a figure that is not flat, it is three-dimensional.  Some examples of 3-D solids include a cube, rectangular prism, cone, cylinder, pyramid, sphere and so on.  Once your child has had an opportunity to explore various 3-D solids, she will be ready to begin looking at the main components of 3-D solids: faces, edges and vertices.

Faces

A face is a flat surface on a 3-D solid.  Students are often asked to identify the number of faces on 3-D solids.  It is important to note that a face must be flat, so a sphere technically does not have a face, it has a curved surface.  Another noteworthy point: Your child may also learn about a base.  A base is a special kind of face.  Cylinders and prisms actually have two bases that are both parallel and congruent.

Edges

An edge is a line segment where two faces meet.  To help my students better understand edges, I ask them to run their finger along the edge of a tissue box.  Try challenging your child to try to find all the edges on a box. Identifying the edges of 3-D solids is typically more difficult for students.

Vertices

“Vertices” is the plural of one vertex.  Vertices are corner points.  Vertices are found where edges meet.

Here is a chart with the numbers of faces, edges and vertices of some common 3-D solids.  Please note that your child may not learn all of these solids at one time.

3-D Solid FACES EDGES VERTICES
CUBE 6 12 8
RECTANGULAR PRISM 6 12 8
CYLINDER 2 0 0
CONE 1 0 0
SQUARE PYRAMID 5 8 5
TRIANGULAR PRISM 5 9 6
SPHERE 0 0 0
TRIANGULAR PYRAMID (TETRAHEDRON) 4 6 4
HEXAGONAL PRISM 8 18 12

What to Watch For:

  • Children often confuse 3-D solids (sometimes called 3-D shapes) with 2-D shapes.  They often learn about shapes (square, rectangle, triangle, pentagon, hexagon, octagon, rhombus, trapezoid, etc…) at the same time as 3-D solids, which can also be confusing.  Be sure your child understand the concept that   3-D solids have 3 dimensions.  You will likely need to explain what 3-dimensional means (length, width, and height).

WANT MORE?

  • As always, playing math games at home is a great way to reinforce math skills learned in school.
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