Last Updated：2025/12/31
Sentence
The
octagonal
projection
of
the
regular
24-cell
(3,4,3}
reveals
that
the
24
vertices
of
this
4-dimensional
polytope
can
be
distributed
as
16
+
8:
the
16
vertices
of
the
4-cube
γ₄
=
{4,3,3}
and
the
8
vertices
of
its
dual,
the
16-cell
β₄
=
{3,3,4}.
This
view
of
the
24-cell
is
less
well-known
than
the
dodecagonal
projection,
in
which
the
β₄
appears
as
two
squares
of
different
sizes
joined
by
8
equilateral
triangles.
Quizzes for review
The octagonal projection of the regular 24-cell (3,4,3} reveals that the 24 vertices of this 4-dimensional polytope can be distributed as 16 + 8: the 16 vertices of the 4-cube γ₄ = {4,3,3} and the 8 vertices of its dual, the 16-cell β₄ = {3,3,4}. This view of the 24-cell is less well-known than the dodecagonal projection, in which the β₄ appears as two squares of different sizes joined by 8 equilateral triangles.
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