Definition:Rhombohedron

Definition

A rhombohedron is a parallelepiped each of whose faces is a rhombus:

Hence it is a parallelepiped whose edges are all the same length.

Also defined as

Some sources define a rhombohedron to be a parallelepiped whose faces are all oblique parallelograms.

Thus the criterion for all the edges to be the same length is not required to hold.

The Penguin Dictionary of Mathematics defines a rhombohedron to be a hexagonal prism, but this is surely a mistake.

Also see

• Results about rhombohedra can be found here.

Linguistic Note

The plural of rhombohedron is properly rhombohedra, although the technically less correct form rhombohedrons can also be seen

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): rhombohedron
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): rhombohedron

• Weisstein, Eric W. "Rhombohedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Rhombohedron.html