by
Bathsheba
There are six regular convex polytopes in 4D, which are analogous to the
five Platonic solids in 3D. This is the fifth, the hyperdodecahedron, a remarkably beautiful object brought to my attention
by George Hart.
Here it's shown in a Schlegel diagram so you can see all 120 dodecahedral cells, though most are transformed by perspective: in this projection, the only regular dodecahedra are the biggest one on the outside and the tiniest one at the center.
A bigger model is here.
Here it's shown in a Schlegel diagram so you can see all 120 dodecahedral cells, though most are transformed by perspective: in this projection, the only regular dodecahedra are the biggest one on the outside and the tiniest one at the center.
A bigger model is here.
by
Bathsheba
There are six regular convex polytopes in 4D, which are analogous to
the five Platonic solids in 3D. This one is the odd polytope out, the one without a 3D counterpart.
It has 24 octahedral cells, all shown in this Schlegel diagram. Like the pentachoron it's self-dual -- the only self-dual solid in any dimension > 2 that is not a simplex. And if that wasn't enough, it's also the only regular convex polytope in any dimension > 2 that tiles its space and is not a hypercube.
It has 24 octahedral cells, all shown in this Schlegel diagram. Like the pentachoron it's self-dual -- the only self-dual solid in any dimension > 2 that is not a simplex. And if that wasn't enough, it's also the only regular convex polytope in any dimension > 2 that tiles its space and is not a hypercube.
by
Bathsheba
The BBC feature The Code, which aired in the summer and fall of 2011, culminated in a treasure hunt. This is the treasure. The original was made in bronze-finish steel and silver; this recoloured model shows the structure. It is a rendering of the five Platonic solids, nested.
An uncoloured version is here.
An uncoloured version is here.
