The first animations truncate a regular polyhedron to the mid-points
of its edges, then switch to the dual model and truncate back
from the mid-points of its edges.
The second animations show the full range of an idealised truncation.
The edges are treated as lines rather than line segments. The edges
are cut in a ratio that ranges from -infinity to +infinity.
At the
extremes of the range the circumsphere of the model grows to become
infinitely large. In order to view the transformation the truncated model
is scaled to maintain the circumsphere at a constant size. The effect on
the base polyhedron is to shrink it into the centre at the
extreme ratios.
The animations were made with the following scripts
Transformation between a tetrahedron and a dual tetrahedron by
truncating to the mid-points of the edges and then switching models.
view animation (1.0Mb)
Transformation between an icosahedron and a dual dodecahedron by
truncating to the mid-points of the edges and then switching models.
view animation (2.2Mb)
Transformation between a great dodecahedron and a dual small stellated
dodecahedron by
truncating to the mid-points of the edges and then switching models.
view animation (1.7Mb)
Transformation between a great icosahedron and a dual great stellated
dodecahedron by
truncating to the mid-points of the edges and then switching models.
view animation (1.4Mb)
An idealised truncation of a
tetrahedron
from -infinty to +infinity.
The model is scaled to have a circumsphere of constant size.
The tetrahedron does not have central symmetry, and hence the limit of
truncation at the two extreme ratios produces different models. This
is seen as a break in the animation cycle at the switch from +infinity
to -infinity.
view animation (1.4Mb)
An idealised truncation of a
octahedron
from -infinty to +infinity.
The model is scaled to have a circumsphere of constant size.
view animation (1.9Mb)
An idealised truncation of a
icosahedron
from -infinty to +infinity.
The model is scaled to have a circumsphere of constant size.
view animation (2.8Mb)
An idealised truncation of a
dodecahedron
from -infinty to +infinity.
The model is scaled to have a circumsphere of constant size.
view animation (2.8Mb)
An idealised truncation of a
small stellated dodecahedron
from -infinty to +infinity.
The model is scaled to have a circumsphere of constant size.
view animation (2.6Mb)
An idealised truncation of a
great dodecahedron
from -infinty to +infinity.
The model is scaled to have a circumsphere of constant size.
view animation (2.6Mb)
An idealised truncation of a
great stellated dodecahedron
from -infinty to +infinity.
The model is scaled to have a circumsphere of constant size.
view animation (3.0Mb)
An idealised truncation of a
great icosahedron
from -infinty to +infinity.
The model is scaled to have a circumsphere of constant size.
view animation (2.9Mb)
