Equilateral triangle
Cut through the far ends of the three edges that meet at one vertex. Each side is a face diagonal, so all three sides are equal.
Open in 3D →Cutting a cube — what shape is the cross-section?
Slice a cube with a plane through three points and the cross-section can take many shapes. Here are the nine classic cases. Each figure has an “Open in 3D” button that sets up the same cut in the app, where you can rotate it, measure it and print its net.
Nine cross-sections
The black dots are the three points the plane passes through.
Isosceles triangle
Of the three edges at one vertex, pass through the ends of two and the midpoint of the third. Two sides come out equal.
Open in 3D →Square
A plane parallel to a face gives a square equal to that face.
Open in 3D →Rectangle
Cut through two opposite parallel edges. The section is 1 by a face diagonal.
Open in 3D →Rhombus
Cut through two opposite vertices (the ends of a space diagonal) and the midpoint of an edge. All four sides are equal.
Open in 3D →Parallelogram
Cut through two opposite vertices and a point one third along an edge. Moving the point away from the midpoint turns the rhombus into a parallelogram.
Open in 3D →Isosceles trapezoid
Cut through the midpoints of two top edges and a bottom vertex. The top and bottom faces are parallel, so the section's top and bottom sides are parallel too.
Open in 3D →Pentagon
Cut through the midpoints of two top edges and the farthest bottom vertex. The plane crosses five faces, so the section is a pentagon (never a regular one).
Open in 3D →Regular hexagon
Cut through the midpoints of three edges chosen so that the plane crosses all six faces: it joins six edge midpoints into a regular hexagon.
Open in 3D →Three rules for drawing a cross-section
- Join two points on the same face
The section's sides lie on the cube's faces. Two points on the same face are joined by a straight line — that is a side of the section. - Parallel faces give parallel sides
The lines on opposite faces (say top and bottom) are always parallel. Use this to find the missing sides. - Extend lines to find intersections
If no face has two known points, extend a section line or a cube edge outward and use where they meet.
FAQ
- What is the most sides a cube's cross-section can have?
- Six. A face can hold at most one side of the section and a cube has six faces, so there is no heptagon or more.
- Can the cross-section be a regular pentagon?
- No. A pentagon is possible, but sides on opposite faces are parallel, which rules out a regular pentagon.
- When is the cross-section a regular hexagon?
- When the plane passes through the center perpendicular to a space diagonal — it goes through six edge midpoints.
- Can the cross-section be a right triangle?
- No. A triangular section around a vertex always has three acute angles.
Try it yourself
In the app you can click vertices or split edges into thirds and cut through any three points. The shape's name, side lengths and area are shown automatically.
Open the app