Definition:Icosahedron

Definition

An icosahedron is a polyhedron which has $20$ faces.

Regular Icosahedron

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

Truncated Icosahedron

A truncated icosahedron is an Archimedean polyhedron which has $32$ faces:

$20$ regular pentagons

$12$ regular hexagon

It has:

$90$ edges

$60$ vertices, each of which is the meeting point of $1$ regular pentagon with $2$ regular hexagons

A truncated icosahedron is formed by truncating a regular icosahedron so that the vertices lie $\dfrac 1 3$ of the way along the edges of the regular icosahedron.

Also see

• Results about icosahedra can be found here.

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): $20$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): icosahedron
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $20$
• 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)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): icosahedron (icosahedra)