Stella: Polyhedron Navigator

"If you're unfamiliar with three-dimensional polyhedra, Great Stella gives you the chance to get acquainted in the on- and off-screen worlds"
Mike Bedford, PC Plus magazine, Issue 271, August 2008, p46
"I am finding Great Stella the greatest program ever devised for the use of polyhedron model makers..."
Fr. Magnus Wenninger (author of "Polyhedron Models") [Read more testimonials]

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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 models out of paper. Small Stella has a fixed list of built-in models and can print out nets for over 300 polyhedra. Great Stella is more advanced, with many more built-in models, and tools for creating literally trillions of new ones. Stella4D includes everything from Great Stella, but adds support for 4D polytopes too. 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.

Finally, MoStella Free, MoStella Silver and MoStella Gold are mobile apps which allow you to carry a large collection of polyhedra in your pocket wherever you go!


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:

    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.
  • Built-in models:
    • 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)
  • Duals of the above polyhedra. (Lookup dual in glossary).
  • Nets: (Lookup net in glossary).
    • 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).

See screen shots.
Download free demo version of Small Stella.
Purchase full version of Small Stella.


Great Stella download | purchase | compare products

Great Stellais 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:

  • 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.
  • Duals of any model are available.
  • Nets for dual-morphed models can be printed.
  • Compounds of polyhedra with their duals (including nets).
  • Stellations (see example photos):
    • 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).
See screen shots.
Download free demo version of Great Stella.
Purchase full version of Great Stella.
See what customers say about Great Stella.


Stella4D download | purchase | compare products

Stella4Dexpands 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:

  • 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 all of these.
    • A separate category groups all the convex polychora together.
    • Any uniform duoprism or antiduoprism can be created.
    • Various uniform fissaries, scaliforms, and compounds are also included.
  • Duals of any polychoron are available.
  • Compounds of polychora with their duals.
  • 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.
See screen shots.
Download free demo version of Stella4D.
Purchase full version of Stella4D.
See what customers say about Stella4D.


MoStella

Carry polyhedra wherever you go!

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.



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