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Tetrahedron vs Triangular Pyramid in 3D

These are two names for the same family of solids. Every tetrahedron is a triangular pyramid, with four triangular faces. A regular tetrahedron adds a stricter rule: all six edges are equal, so all four faces are equilateral triangles.

Explore This Comparison
Same Family.Regular is the extra condition.

Regular Tetrahedron

All six edges are equal.

Complete 3D regular tetrahedron

h = a√(2/3)

Triangular Pyramid

Change the height and apex.

Complete 3D triangular pyramid

V = Bh / 3

Drag to rotate · Scroll or pinch to zoom · Arrow keys rotate the focused model. Switch off Link Rotations to move only one shape.

Tetrahedron = Triangular Pyramid. The first name counts four faces; the second describes a triangular base and an apex. Move the apex above and sideways to see what changes.

4 faces6 edges4 vertices
Changing units relabels the numbers.

Both models are tetrahedra. Only the left one is necessarily regular.

The Difference Is “Regular,” Not “Tetrahedron”

A Tetrahedron

Any non-degenerate solid bounded by four triangular faces. Its triangles do not need to be equal, and its apex need not be above the center of the chosen base.

A Regular Tetrahedron

A tetrahedron with six equal edges and four congruent equilateral faces. It is a Platonic solid. Its height cannot vary independently while its edge length stays fixed.

A Triangular Pyramid

The same general solid viewed as a pyramid. Choose any one of its four triangles as the base; the remaining vertex is the apex. Changing that choice does not change the solid.

One Volume Rule Works for Both

For any triangular pyramid, V = Bh/3. Here B is the chosen base area, and h is the perpendicular distance from the apex to the base plane. Moving the apex sideways at the same height changes the side faces but does not change the volume.

Regular Tetrahedron

Volume7.54 cm3V = a³ / (6√2)
Surface areaS = √3a²
27.71 cm2
Perpendicular heighth = a√(2/3)
3.27 cm
One equilateral faceB = √3a² / 4
6.93 cm2

Adjustable Triangular Pyramid

Volume11.55 cm3V = √3a²h / 12
Surface areaSum of all four triangle areas
37.72 cm2
Lateral areaSum of the three side areas
30.79 cm2
Equilateral base areaB = √3a² / 4
6.93 cm2

The general triangular pyramid need not have an equilateral base. This model uses one to isolate the effect of apex position. Surface areas are calculated from the actual triangles, including when the apex is offset.

Different Triangles, the Same Four-Face Structure

The regular model unfolds into four equal equilateral triangles. The adjustable model keeps four triangles, but the three sides can differ. The gold triangle is the chosen base; it is not an extra face.

Properties and face nets
Property Regular Tetrahedron Triangular Pyramid
Faces 4 congruent equilateral triangles 4 triangles; not necessarily congruent
Edges and vertices 6 edges · 4 vertices 6 edges · 4 vertices
Equal edge lengths All six equal Not required
Possible bases Any of the four faces Any of the four faces
Volume Bh/3; also a³/(6√2) when regular Bh/3 for any triangular base
Flat face nets
Regular Tetrahedron flat net 1 2 3 4
4 faces. Dashed lines are folds.
Triangular Pyramid flat net 1 2 3 4
4 faces. Dashed lines are folds.

Common Questions

Is every triangular pyramid a tetrahedron?

Yes. A triangular base plus three triangular side faces gives exactly four triangular faces. This is a tetrahedron.

Must a tetrahedron have equilateral triangles?

Only a regular tetrahedron must. “Tetrahedron” by itself does not require equal edges or congruent faces.

Is the sloping edge the height?

No. The perpendicular height runs from the apex to the base plane at a right angle. A sloping side edge usually has a different length.

Does an offset apex change the volume?

At fixed base area and perpendicular height, no. The volume stays Bh/3 even when the apex moves sideways. The side areas can change.