"I am finding Great Stella the greatest program ever devised for the use of
polyhedron model makers..."
Fr. Magnus Wenninger (author of "Polyhedron Models")
"This is the first year my 11 year old autistic son has smiled on Christmas
day. Your software, a gift from Santa has made this day possible. Thank you"
Welcome to the Stella
home page! Small Stella,
Great Stella
and Stella4D are computer programs which let
you create and view polyhedra on the screen, then print out the unfolded
nets required to build your own paper models.
Small Stella has a fixed list of built-in
models and can print out nets for over 300 polyhedra.
Great Stella has many more built-in models, and tools for creating literally trillions
of new ones.
Stella4D includes everything from Great Stella, but also adds support for 4D
polytopes. 4D models can be projected into 3D, and you can see their 3D cross-sections
and nets in real-time.
Click here for photos of polyhedra I've made, all
using nets printed from these programs, along with tips for building them.
The programs are fun and easy to use. Some of the jargon in
the descriptions below may be a bit baffling at first, but you don't need to
know anything about maths or geometry to be able to use these programs and
create amazing polyhedra. They should suit everyone from the amateur
enthusiast to the seasoned polyhedral expert! (There's a comprehensive
glossary too, if you do get stuck).
Click here for a feature comparison between
products.
Small Stella can display and print nets
for over 300 polyhedra. You just pick a model, decide what size you want it,
and Stella figures out what nets are required and prints them out. Then
you cut them out, fold them up, and glue them together to build your own
polyhedra! It is ideal for amateur model-makers or as an educational geometry
tool for schools. You can always upgrade to
Great Stella later.
Small Stella Features:
Many models from Small and Great Stella can be easily constructed using
these plastic polygons from GeoAustralia.
Rotate polyhedra on the screen by dragging the mouse with the
left button down. Continuous rotation is also possible by releasing the
button while still dragging the mouse.
Zoom in and out on polyhedra by dragging the mouse with the
right button down (or use the mouse wheel).
Polyhedron faces may be exploded apart by dragging the mouse
with the left button down and the Shift & Ctrl keys pressed.
Print out nets for building any of the above polyhedra. You
just tell it how big the final model should be.
Nets may be grouped by colour for printing onto
different coloured paper, or colours may be mixed for use with a colour
printer.
Tabs are included around nets. Choose from:
Single tab method - glue tabs under connecting faces.
Double tab method - glue tabs to each other,
my recommendation.
Edge connection IDs can be printed on edges of nets,
showing which parts to glue together.
Nets may be viewed folding and unfolding in 3D.
Animated transitions between models.
Design your own polyhedral tours, animated polyhedral
slideshows.
Put images (e.g. photos, drawings or textures) on the faces of
polyhedra. Interactively position, rotate and size them. Then print out
nets which include the images. Make a paper dodecahedron with your pets or
friends' faces on the sides!
Show spheres at the vertices and cylinders along the edges, each with
metallic, stone or wooden finishes.
Geomag rendering mode. Display shapes as if made using
the Geomag magnetic construction kit, with info about how many
balls, rods, and panels are required
(e.g. 1,
2,
3,
4)
An information window tells you how many faces/vertices/edges a
model has, as well as lots of other useful data, such as how many edges
you will have to cut/fold/glue to make a paper model.
Compounds of polyhedra with their duals may be viewed (no nets).
View cross-sections (or slices) through polyhedra.
These make great animations as the slicing depth is changed in
real-time.
Symmetries of any model may be displayed graphically.
Six different techniques for morphing between dual polyhedra
may be viewed in real-time.
Polyhedra may be viewed in
stereoscopic
3D, by using red-green or red-blue glasses, or with the stereo
pair side by side for cross-eyed or wall-eyed viewing.
Vertex figures (with Dorman Luke construction of the
dual face) may be viewed and printed.
Advanced features like measuring the distance between points, lines or
planes in a model, and manually tweaking the nets created.
Multi-level undo/redo.
An intuitive interface means it is both powerful and easy to
use.
Upgrade to Great Stella later (scroll down to see Great Stella
features, see purchase page for pricing).
Great Stella is the ultimate tool for creating, visualising, and printing nets
for polyhedra. See my paper
Stella: Polyhedron Navigator for a
detailed account of what it can do.
Includes all features from Small Stella
(see above).
Built-in models (in addition to those from Small Stella):
Any regular-faced prisms and antiprisms (not just
the convex ones. See photos)
Any regular-faced pyramid, cupola, cuploid or
cupolaic-blend (see example photo)
A library of over 400 other models is also included, created using
the tools available in
Great Stella. This contains most
of Brückner's 1906 polyhedra, and has a category for
compounds (see example photos),
including:
2, 4, 5, 6, 8, 10, 20 and 40 tetrahedra.
2, 3, 4, 5, 6, 8 and 20 cubes/octahedra.
2, 5 and 8 dodecahedra/icosahedra.
2 and 5 small stellated dodecahedra/great dodecahedra/great
stellated dodecahedra/great icosahedra.
3, 4 and 5 cuboctahedra.
2 and 5 icosidodecahedra.
4, 5 and 20 tetrahemihexahedra.
and many many more.
Duals of any model are available.
Nets for dual-morphed models can be printed.
Compounds of polyhedra with their duals (including nets).
Any model may be stellated, leading to trillions of new
polyhedra. For example, the 59 icosahedra, the 227
triacontahedra, and stellations from Magnus Wenninger's
Polyhedron Models book.
Stellation is very fast, and generally takes less than a
second for even the most complex uniform polyhedron.
By default, stellation cells are automatically chosen to recreate
the original uniform polyhedron. This makes nets for uniform
polyhedra easy to obtain, and would be difficult and time-consuming
to do by hand.
Support for certain stellation criteria (eg fully
supported or Miller's rules), so that you can easily
iterate over all the valid stellations of some polyhedron, without
having to manually select the appropriate cells for each model in
the set. When using "Miller's rules", just hit the Up
Arrow 59 times to see all the 59 icosahedra.
Stellation diagrams and cell diagrams may be viewed
and printed.
Stellation from an arbitrary set of planes.
Facetings: Any model may be faceted to create new
polyhedra (this is the dual process of stellation, see example
photos).
Automatically step through valid facetings according to your
selected criteria.
Polyhedra can be augmented/excavated/drilled
using any other polyhedron. Use this to glue lots of models together,
create more Stewart toroids, or explore many other creative avenues.
The convex hull or convex core of any model can be
created.
A zonohedron can be created based on any model.
A geodesic sphere can be created based on most models.
Waterman polyhedra.
Symmetry:
The symmetry group of any model is automatically
established, and symmetries may be displayed graphically.
The user may choose from a list of all possible
sub-symmetry groups for any model. This may change the
colouring of a model, and affects stellation, faceting, and
augmentation/excavation/drilling.
Print out nets for building any of the above polyhedra
(except infinite dual polyhedra). You just tell it how big the
final model should be.
Extra polygons may be created and printed for use as extra internal
support inside a model.
Export anti-aliased 2D images and videos in various formats.
Create AVI videos or animated GIFs.
Create seamless repeating videos.
Create videos of polyhedral tours.
Create videos of a polyhedron animated in various ways: rotating,
morphing into its dual and back, folding and unfolding etc.
Preview animation before exporting.
Polyhedra may be exported to DXF,
POV-Ray (a free ray-tracer),
VRML, Wavefront OBJ, OFF or STL format.
Import closed 3D models from OFF format.
Any alternative names are given for all uniform/dual polyhedra, as
well as their reference and page numbers in Wenninger's
Polyhedron Models and Dual Models, making this the
ultimate reference for the uniform/dual polyhedra.
Upgrade to Stella4D later (scroll down to see Stella4D
features, see purchase page for pricing).
Stella4D expands on Great Stella to include four-dimensional polytopes,
known as polychora. See 3D cross-sections animating in real-time, see complete
polychora projected into 3D and try 4D rotation, and view 3D nets and vertex figures of
4D polytopes.
Includes all features from Great Stella
(see above).
Built-in models (in addition to those from Great Stella):
All 16 regular polychora.
All 1849 known uniform polychora. This is the only place
you can see and interact with all of these. [Edit: some new uniform
polyhedra have been discovered since the last version of Stella was released!
These should appear in a future version]
A separate category groups all the convex polychora
together.
Any uniform duoprism or antiduoprism can be created.
View 4D models projected into 3D (perspective or orthogonal,
with or without back-cell or front-cell removal).
Interactively rotate the projection direction, or choose cell-first,
face-first, edge-first or vertex-first. The default auto setting usually
finds the projection giving the greatest symmetry.
View 3D cross-sections of 4D polytopes.
Interactively change the slicing depth in real time.
Slice cell-first, face-first, edge-first or vertex-first.
Interactively rotate the slicing plane.
See how the cross-section fits into the 3D projection of the
original 4D model.
Snap the cross-section depth to the nearest vertex, and step
through the depths where the plane hits a vertex.
Show small spheres when true vertices are close to the slicing
plane.
Color cells along the slicing direction to create more colorful
slices.
View 3D nets of 4D polytopes. Manually rearrange the cells in
the net.
View 3D vertex figures and individual 3D cells of 4D polytopes.
You may use the model from any view as the new 3D base model (for
creating nets, stellations etc). This includes 3D cross-section, 3D nets,
3D projections of 4D models, 3D vertex figures, or individual 3D cells.
Truncate, rectify, and expand 4D polytopes.
Create convex hulls or convex cores of 4D polytopes.
Delete or keep just one part of a 4D compound.
Create 4D prisms from 3D polyhedra.
Create 4D step prisms and gyrochora.
Create 4D Waterman polychora.
Two different techniques for morphing between dual polychora
may be viewed in real-time.
When displaying using spheres and cylinders, their size will vary
correctly according to the 4D projection (spheres further away in 4D will
appear smaller in a perspective projection).
Most of Great Stella's colouring and hiding options for faces are
supported for cells in 4D. Undo/redo, memory slots and Measurement Mode
are also supported.
Import any 4D model in 4D OFF format. An example is given
in the manual.
Carry polyhedra wherever you go!
NOTE: unfortunately Google changed their guidelines and no longer allow these apps
on most modern devices, and I can't rebuild them because the dev tools I used are now
defunct, so these are in limbo until I can rewrite them another way.
MoStella Free
Android app for rotating polyhedra in 3D, viewing their duals, and morphing
between duals etc. Includes Platonic solids, Kepler-Poinsot and Archimedean
solids.
MoStella Silver
Android app. Includes everything from MoStella Free, plus all the uniform
polyhedra and no ads.
MoStella Gold
Android app. Includes everything from MoStella Silver, plus many more
categories of polyhedra including The 59 Icosahedra, stellations, compounds,
Johnson solids, near misses, Stewart toroids, geodesic spheres, etc.