Definition:Icosahedron/Regular

Definition

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

Occasionally an author may refer to a regular icosahedron as just an icosahedron, glossing over the fact of its regularity.

It is wise to make sure of what is meant.

Also see

• Definition:Platonic Solid
• Definition:Deltahedron

• 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.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $5$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $8$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): icosahedron
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Platonic solid
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.4$: Euclid (flourished ca. $300$ B.C.)
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $8$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): icosahedron (plural icosahedra)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): icosahedron (plural icosahedra)
• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $2$: The Logic of Shape: Euclid
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Platonic solid: $\text {(v)}$