Stella: Polyhedron Navigator
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).
Small Stella download | purchase | compare 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: (click to open)
Many models from Small and Great Stella can be easily constructed using these plastic polygons from GeoAustralia.- Platonic solids (see photos)
- Archimedean solids (see photos)
- Kepler-Poinsot solids (see photos)
- Convex Prisms and antiprisms (see photos)
- Johnson solids (non-uniform regular-faced convex polyhedra, see example photos)
- "Near misses" (models that are almost Johnson solids)
- Stewart toroids (regular-faced polyhedra with holes, see example photos), and Stewart's G3, Z4, X and K4' models
- Five popular compounds (5 cubes, 5 octahedra, 2/5/10 tetrahedra)
- A collection of geodesic domes (including geodesic spheres and geodesic hemispheres)
- 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.
Great Stella download | purchase | compare products
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.
Great Stella Features: (click to open)
- Includes all features from Small Stella (see above).
- Built-in models (in addition to those from Small Stella):
- All uniform polyhedra (see photos)
- 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.
- 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.
- Automatically step through valid facetings according to your selected criteria.
- 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.
- 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.
Stella4D download | purchase | compare products
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.
Stella4D Features: (click to open)
- Includes all features from Great Stella (see above).
- Built-in models (in addition to those from Great Stella):
- All 16 regular polychora.
- Any uniform duoprism or antiduoprism can be created.
- All 1849 known uniform polychora (aside from the infinite duoprism/antiduoprism sets). Stella4D is the only program where you can load and interact with every one of these. [Edit: some new uniform polychora have been discovered since the last version of Stella was released! These will appear in a future version]
- A separate category groups all the convex polychora together.
- Various uniform fissaries, scaliforms, and compounds are also included.
- 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.
MoStella
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.