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A regular icosahedron is an icosahedron whose $20$ faces are all congruent equilateral triangles.

The regular icosahedron is an example of a deltahedron.

Also known as

It is commonplace for authors to refer to a regular icosahedron as just an icosahedron, glossing over the fact of its regularity.

Also see

  • Results about regular icoashedra can be found here.

Historical Note

In The Elements, this object is referred to just as an icosahedron.

In the words of Euclid:

An icosahedron is a solid figure contained by twenty equal and equilateral triangles.

(The Elements: Book $\text{XI}$: Definition $27$)

According to the Pythagorean tradition, the regular icosahedron was the symbol for the element water.

Linguistic Note

The word icosahedron derives from the Classical Greek εἰκοσάεδρον:

eíkosi (εἴκοσι), meaning twenty
hedron (a form of ἕδρα), meaning base or seat.

The technically correct plural of icosahedron is icosahedra, but the word icosahedrons can often be found.