by

**Thanks to the work of
Scott Vorthmann this website is fully functional for the first time in
years.
The 3-D images (including the one above) are generated using VRML.
Browser support for this technology disappeared in the early 2000s.
Thanks to the X_ITE team and Scott's coding, this and other VRML based
sites can now be enjoyed once more as intended.
Scott's VRML Revival project page can be found at vorth.github.io/vrml-revival/
**

** HEDRON:** Polyhedron generating software, now at V1.12,
available here. Help text here.
Hedron
Tools (Release 2B).

**Uniform Polyhedra:** Displayed
as
'switchable'
VRML
files,
including
Skilling's figure, including links to 'molecular' VRML files of all the
uniform Polyhedra.

**Johnson
Solids:** More 'switchable' VRML files, plus some isomorphs to the Johnson Solids.

**Rhombohedra:** Polyhedra containing rhombic faces:

- Isohedral Rhombohedra
- Convex Rhombic Polyhedra with Icosahedral Symmetry
- Convex Polyhedra containing Rhombi as found in the Rhombic Dodecahedron
- Convex Polyhedra containing Golden Rhombi
- Variations on a Rhombic Theme (non convex isomorphs to the above)
- The
Rhombic Enneacontahedron and partial zonohedrifications of the
Dodecahedron
- The
Great Rhombic Enneacontahedron
- Bi-Rhombic
Polyhedra
with
Icosahedral
Symmetry
- Dissecting the Expanded Rhombic Dodecahedron
- Dissecting the Rhombic Triacontahedron
__Rhombified Stellations of Snub Uniform Polyhedra____,__- Rhombically Expanded Deltahedra
- Cupolaic Expanded Rhombohedra and
- Molybi Augmented Polyhedra

**Isohedral
Deltahedra**:
Face transitive polyhedra consisting of
equilateral triangles.

**Elementary
Honeycombs:** Vertex transitive space filling
honeycombs with non-uniform cells.

**Acrohedra:** UPDATED
Polyhedra with a specified vertex, n-n-3
acrons, n-4-3-3 acrons, n-6-3 acrons, n-6-4 acrons, some near misses (with 'Stress
Maps') and tables of dihedral angles.

**Petrie
Expanded Polyhedra:**
Polyhedra that have been expanded across their Petrie Polygons

**Convex Segmentochora:** Dr Richard Klitzing's models of 4-dimensional
figures confined to two hyper-planes. Includes VRML models of all figures.

**Polyhedral
'Twisters':** Animations of an
unusual deformation between uniform polyhedra.

**Tessellations
of
the
Plane:** Uniform
polygonal tessellations of the plane and hyperbolic star
tessellations.

**Locally convex octahedral and icosahedral polyhedra:** Locally convex polyhedra with high degrees of
symmetry.

**Locally
Convex Prismatic Polyhedra:** Commentary
and models of

- snub anti-prisms: an infinite family of 2-regular prismatic polyhedra
- bi-snub anti-prisms: an infinite family of 3-regular prismatic polyhedra
- spheno-prisms: an infinite family of prismatic polyhedra based on the sphenoid
- elongated spheno-prisms: the above family can be elongated by the insertion of square faces
- gyro-elongated spheno-prisms: the sphenoprisms can also be gyro-elongated, a disphenocingulum is among the results
- n-4-3-3 polyhedra: a family of prismatic polyhedra containing n-4-3-3 vertices

**Chiral
Prismatic Polyhedra: ** Commentary and models of

- tetrakis snub prisms: adding pyramids to the faces of a snub cube results in an infinite family of polyhedra
- pentakis snub pentaprisms: the same happens when pyramids are added to the faces of a snub dodecahedron
- cingulated anti-prisms: possibly the simplest family of chiral prismatic polyhedra
- see also n-4-3-3 polyhedra
above

**Cupolas
and
Semicupolas:** Polyhedra based on the
cupola with emphasis on the great
rhombicosidodecahedron and the ditrigonary
polyhedra.

**Sphenocoronal
Polyhedra:** Families of prismatic
polyhedra based on the

- Szilassi and Császár polyhedra,
- some of the simpler Stewart Toroids
- a focus on the "K4-World" and
- the "T5-Country",
- Toroids formed from augmented duals of uniform polyhedra
- Canonical Toroids

**Edge
Expanded Prismatic Polyhedra:** Edge Expanded Biprisms and Bi-antiprisms. A generalisation of the
'spheno-prisms'.

**Isomorphs
of
the
Icosahedron:** Polyhedra
generated from an icosahedral net.

**Isomorphs
of
the
Rhombicuboctahedron:** Polyhedra
generated from a rhombicuboctahedral net, with animated VRMLs.

**Phi in the
Icosahedron and Dodecahedron:**
A
simple
method
of
generating
vertex
co-ordinates
using
the Golden
Ratio

**Miscellaneous
Polyhedra:** Including models of the Stewart G3, the self
augmented
heptagonal
antiprism the Edshammar
polyhedron and the associahedron

**Near
Misses:** Polyhedra that are not quite
regular, including near-misses
to the Johnson Solids (the '**A**-list') and acrohedral near
misses amongst others.

This site is designed
primarily to provide some form of ordered access to the many VRML
models of polyhedra I have made over the past few years, mainly using
my programme "**HEDRON**" (which I have
made available). **HEDRON** was used to generate most of the
models shown on this site.

I am not a professional mathematician, and as a consequence this site is as much a catalogue of models than a site providing any great mathematical insight. I have tried to be original in my modelling and I present here a large number of models that I have not seen elsewhere.

At times, I have modelled a polyhedron for which, to my knowledge, no formal name exists. In these cases I have tried to extend existing naming conventions. Where this is the case I have tried to make it clear. Any errors and omissions are mine.

No part of this site may be used for commercial purposes without the express permission of the author.

Any comments or questions
regarding this site? Email me at: *jimhedron@o........*
(see the url of this page for the rest)

**Jim McNeill**