Polyhedra
Polyhedra are used in many domains, including graphics to represent general shapes and geometry to represent solid regions. Polyhedra are simple yet powerful enough to approximate essentially any 3D solid. The Wolfram Language provides comprehensive support for polyhedra representation, visualization and computation. All the common definitions of polyhedra can easily be used, and polygons are deeply integrated in the system, including graphics and geometry.
Polyhedron — polyhedron or collection of polyhedra with or without voids
Graphics »
Graphics3D — visualize polyhedra in 3D with different styles
GraphicsComplex ▪ VertexColors ▪ VertexNormals ▪ EdgeForm ▪ FaceForm
Polyhedron Representation
CanonicalizePolyhedron — convert to a canonical polyhedron representation
PolyhedronCoordinates ▪ OuterPolyhedron ▪ InnerPolyhedron
Cube ▪ Dodecahedron ▪ Icosahedron ▪ Octahedron ▪ Tetrahedron
Cuboid ▪ Hexahedron ▪ Parallelepiped ▪ Prism ▪ Pyramid ▪ Simplex
General Polyhedron Classes
RandomPolyhedron — generate different classes of random polyhedra (convex, simple, etc.)
PolyhedronDecomposition — decompose a polyhedron into different classes of polyhedra
UniformPolyhedron — generate uniform polyhedra (Platonic solids, prisms, etc.)
PolyhedronData — curated collection of polyhedra and their properties
SimplePolyhedronQ ▪ ConvexPolyhedronQ
Polyhedron Operations
DualPolyhedron — dual of a polyhedron
AugmentedPolyhedron — augmented polyhedron
BeveledPolyhedron — beveled polyhedron
TruncatedPolyhedron — vertex-truncated polyhedron
Measures »
Volume — give the volume of a polyhedron
SurfaceArea — give the surface area of a polyhedron
PolyhedronGenus — give the genus of a polyhedron
EulerCharacteristic — give the Euler characteristic of a polyhedron
RegionMeasure ▪ RegionCentroid ▪ RegionMoment ▪ MomentOfInertia ▪ ...
Operations »
RegionUnion, RegionIntersection — union, intersection operations on polyhedra
Rotate, Translate, Scale — geometric transformations of polyhedra
RegionDifference ▪ BooleanRegion ▪ TransformedRegion ▪ ...
Membership
RegionMember — test membership or give conditions for membership
RegionEqual ▪ RegionDisjoint ▪ RegionWithin ▪ RandomPoint
Distance »
RegionDistance — minimum distance from a point to a polyhedron
RegionNearest ▪ SignedRegionDistance ▪ ...
Mesh Parts & Components »
MeshCells — vertices, edges and faces of the polyhedron
ConnectedMeshComponents — split a polyhedron into connected components
MeshPrimitives ▪ MeshCellCount ▪ DimensionalMeshComponents ▪ ...
Region Representation »
Region — geometric representation and automatic visualization of polyhedra
BoundaryMeshRegion ▪ ImplicitRegion ▪ ConstantRegionQ ▪ ...
Solving with Polyhedra »
Solve — find curve crossings etc.
NSolve ▪ Reduce ▪ Minimize ▪ NMinimize ▪ Integrate ▪ NIntegrate ▪ ...
Import and Export »
"STL" — import and export polyhedra