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dodecahedral

Dodecahedral is an adjective relating to a dodecahedron, a regular polyhedron with twelve regular pentagonal faces. In a dodecahedron, three faces meet at each vertex, and all faces are congruent pentagons. It is one of the five Platonic solids and is denoted by the Schläfli symbol {5,3}.

The solid has 12 faces, 30 edges, and 20 vertices. Its dual polyhedron is the icosahedron, which

A common coordinate model uses the golden ratio φ = (1+√5)/2. In this model, a centered dodecahedron can

The term dodecahedral is used in mathematics to describe objects or structures that have a dodecahedral relation

has
20
triangular
faces
and
12
vertices.
The
symmetry
of
the
dodecahedron
is
the
icosahedral
group,
with
full
symmetry
order
120
and
a
rotational
subgroup
of
order
60.
At
every
vertex,
three
pentagonal
faces
meet,
giving
the
vertex
configuration
5.5.5.
be
realized
with
vertex
coordinates
given
by
all
even
permutations
of
(±1,
±1,
±1)
together
with
the
12
permutations
of
(0,
±1/φ,
±φ).
or
symmetry,
and
it
appears
in
discussions
of
polyhedral
geometry,
modeling,
and
related
design
contexts.