Definition:Icosahedron

From ProofWiki
Jump to navigation Jump to search

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

TruncatedIcosahedron.png

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