Free printable 3D shapes chart

Grades K–3Cube, cuboid, prism, pyramid, cylinder, cone and sphere — with the faces, edges and vertices for each one and what the words actually mean. Print it for the wall, or tap through the solids below and count them yourself.

3D Shapes math chart for kids Tap the chart to open it at full size

Nine solids, counted

Every solid shows its faces, edges and vertices. Tap one for the full count and a note on what makes it what it is.

The three with curved surfaces behave differently, and that is worth separating out with the filter. A sphere has no flat faces, no edges and no corners at all, which children find either obvious or impossible depending on how the words were introduced.

For the six made only of flat faces, add the faces to the vertices and take away the edges. The answer is always 2. A cube gives 6 + 8 − 12 = 2, a tetrahedron gives 4 + 4 − 6 = 2. It works for every solid made of flat faces with no hole through it, and showing a child that pattern is a much better use of the chart than making them memorize nine sets of numbers.

Show

Faces, edges and vertices
Tap any solid above
Euler’s check
—

F is faces (a curved surface counts as one), E is edges, V is vertices — the corners.

How to use this 3D shapes chart at home

Put real objects in their hands. A tin is a cylinder, a cereal box is a rectangular prism, a ball is a sphere, a party hat is a cone. Solids are the one topic where a picture is genuinely a poor substitute, because the whole point is the third dimension and a page does not have one.

Count by touching. Run a finger along each edge, press each corner, lay a palm on each face. Children who count faces by looking at a drawing miss the back ones every single time; children who turn an object in their hands do not.

Then unfold something. Cut open an empty cereal box along its edges and lay it flat. Six rectangles, and every edge that was shared becomes a fold. Nets stop being an abstract exercise the moment a child has made one from a real box.

The one rule that ties them together

For any solid made of flat faces, the faces plus the vertices minus the edges always equals 2. Cube: 6 + 8 − 12. Square pyramid: 5 + 5 − 8. Tetrahedron: 4 + 4 − 6. Every time, 2.

It is called Euler's formula, and it is genuinely surprising — there is no obvious reason why stretching or squashing a solid, or adding faces, should leave that combination untouched. It holds for every solid of this kind without a hole through it; a solid shaped like a picture frame gives 0 instead.

For a child this has a practical use as well as a pleasant one: it is a way to check your own counting. If the numbers do not come to 2, a face or an edge has been missed, and it is usually one of the faces round the back.

Prisms, pyramids and the ones with curves

A prism has two identical ends and is the same shape the whole way along. Slice it anywhere across its length and you get the same face. It takes its name from those ends — a triangular prism has triangular ends, a hexagonal prism hexagonal ones.

A pyramid has one base and rises to a single point. It also takes its name from its base, but it changes as you go up, getting smaller until the faces meet. A square pyramid and a triangular prism are easy to confuse from a drawing and impossible to confuse in your hand.

Cylinders, cones and spheres are the odd ones out because they have curved surfaces, which is why their edge and corner counts are so small. A sphere has none at all. They also break Euler's rule, which is a fair thing to point out rather than quietly ignore.

Where 3D shapes usually go wrong

Missing the hidden faces. Counting four faces on a cube because two are out of sight. Turning a real object fixes this instantly and a worksheet does not.

Using 2D names for 3D shapes. Calling a cube a square, or a sphere a circle. The flat name describes one face of the solid, not the solid itself, and it is worth correcting gently every time.

Confusing edges with faces. An edge is a line, a face is a surface. Children counting quickly tend to blur them, which is exactly where Euler's check earns its keep.

Assuming every pointed solid is a pyramid. A cone comes to a point too, but it has a curved surface and a circular base, so it is not a pyramid. Pyramids are made entirely of flat triangles.

After the chart goes up

A chart explains the idea but gives a child nothing to do. These do the rest.

Everything at this level: Kindergarten math · Grade 1 math · Grade 2 math · Grade 3 math

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Questions parents ask

What are faces, edges and vertices?

A face is a flat surface. An edge is where two faces meet, forming a line. A vertex is a corner where edges meet — the plural is vertices. A cube has 6 faces, 12 edges and 8 vertices, and holding one while counting is far more effective than looking at a picture of one.

How many faces does a cube have?

Six, all of them identical squares. It also has 12 edges and 8 vertices. A rectangular prism has the same counts, because it is a cube that has been stretched — the faces are rectangles rather than squares, but there are still six of them.

Does a sphere have any faces?

Not flat ones. A sphere has a single curved surface, no edges and no vertices. Some textbooks call that curved surface a face, which is why answers vary between one and zero. Worth checking how your child's class counts it, because both appear in workbooks.

What is the difference between a prism and a pyramid?

A prism has two identical ends joined by rectangles, so it is the same shape all the way along — a triangular prism looks like a tent. A pyramid has one base and triangular faces rising to a single point. A prism is named after its ends, a pyramid after its base.

What is the difference between 2D and 3D shapes?

2D shapes are flat and have only length and width — you can draw one exactly. 3D shapes are solid and have depth as well, so a drawing of one is always a bit of a lie, showing faces you could not really see at once. That is why holding actual objects matters so much at this age.

What grade is this 3D shapes chart for?

Kindergarten through Grade 3. Naming solids and matching them to everyday objects comes first, counting faces, edges and vertices around Grade 1 or 2, and nets and surface area later on.

Is this 3D shapes chart free to print?

Yes. Open it full size and print as many copies as you need for home or a classroom, with no account and no watermark. Reselling it or re-hosting the file elsewhere is not allowed — link to this page instead.