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Stella is a computer program available in three versions (Great Stella, Small Stella and Stella4D). It was created by Robert Webb of Australia. The programs contain a large library of polyhedra which can be manipulated and altered in various ways.
Polyhedra in Great Stella's library include the Platonic solids, the Archimedean solids, the Kepler-Poinsot solids, the Johnson solids, some Johnson Solid near-misses, numerous compounds including the uniform polyhedra, and other polyhedra. Operations which can be performed on these polyhedra include stellation, faceting, augmentation, dualization (also called "reciprocation"), creating convex hulls, and others.
All versions of the program enable users to print nets for polyhedra. These nets may then be assembled into actual three-dimensional polyhedral models of great beauty and complexity.
In 2007, a Stella4D version was added, allowing the generation and display of four-dimensional polytopes (polychora), including a library of all convex uniform polychora, and all currently known nonconvex star polychora, as well as the uniform duals. They can be selected from a library or generated from user created polyhedral vertex figure files.
Stella provides a configurable workspace comprising several panels. Once a model has been selected from the range available, different views of it may be displayed in each panel. These views can also include measurements, symmetries and unfolded nets.
A variety of operations may be performed on any polyhedron. In 3D these include: stellation, faceting, augmentation, excavation, drilling and dualising.
Other features include spring network relaxation, generation of the convex hull, and generation of cupolaic blends and related figures.
In geometry, an Archimedean solid is one of 13 convex polyhedra whose faces are regular polygons and whose vertices are all symmetric to each other. They were first enumerated by Archimedes. The convex polyhedra with regular faces and symmetric vertices include also the five Platonic solids and the two infinite families of prisms and antiprisms; these are not counted as Archimedean solids. The pseudorhombicuboctahedron has regular faces, and vertices that are symmetric in a weaker sense; it is also not generally counted as an Archimedean solid. The Archimedean solids are a subset of the Johnson solids, whose regular polygonal faces do not need to meet in identical vertices.
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meeting at each vertex. Viewed from a corner, it is a hexagon and its net is usually depicted as a cross.
In geometry, a Kepler–Poinsot polyhedron is any of four regular star polyhedra.
In geometry, an octahedron is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex.
In geometry, a polyhedron is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.
In geometry, a polyhedral compound is a figure that is composed of several polyhedra sharing a common centre. They are the three-dimensional analogs of polygonal compounds such as the hexagram.
In geometry, a 4-polytope is a four-dimensional polytope. It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices, edges, faces (polygons), and cells (polyhedra). Each face is shared by exactly two cells. The 4-polytopes were discovered by the Swiss mathematician Ludwig Schläfli before 1853.
In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure. Starting with an original figure, the process extends specific elements such as its edges or face planes, usually in a symmetrical way, until they meet each other again to form the closed boundary of a new figure. The new figure is a stellation of the original. The word stellation comes from the Latin stellātus, "starred", which in turn comes from Latin stella, "star". Stellation is the reciprocal or dual process to faceting.
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that the faces are congruent regular polygons which are assembled in the same way around each vertex.
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. It is a Catalan solid, and the dual polyhedron of the cuboctahedron.
In geometry, a uniform 4-polytope is a 4-dimensional polytope which is vertex-transitive and whose cells are uniform polyhedra, and faces are regular polygons.
A polyhedron model is a physical construction of a polyhedron, constructed from cardboard, plastic board, wood board or other panel material, or, less commonly, solid material.
In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality.
The compound of five cubes is one of the five regular polyhedral compounds. It was first described by Edmund Hess in 1876.
In geometry, faceting is the process of removing parts of a polygon, polyhedron or polytope, without creating any new vertices.
In geometry, a quasiregular polyhedron is a uniform polyhedron that has exactly two kinds of regular faces, which alternate around each vertex. They are vertex-transitive and edge-transitive, hence a step closer to regular polyhedra than the semiregular, which are merely vertex-transitive.
In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular polyhedra in three dimensions and the regular polygons in two dimensions.
In geometry, the first stellation of the rhombic dodecahedron is a self-intersecting polyhedron with 12 faces, each of which is a non-convex hexagon. It is a stellation of the rhombic dodecahedron and has the same outer shell and the same visual appearance as two other shapes: a solid, Escher's solid, with 48 triangular faces, and a polyhedral compound of three flattened octahedra with 24 overlapping triangular faces.
This is quite a sophisticated program for those who want to go beyond the basics.
