(by psl)
Structural form-finding and analysis for Rhino using 3d graphic statics and reciprocal polyhedrons.
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*PolyFrame 2 has been released. It includes all functionalities from PolyFrame as well as a Grasshopper Plug-in with a variety of new features.


PolyFrame is a geometry-based, structural form-finding plugin for Rhinoceros3d based on the principle of the equilibrium of polyhedral frames known as 3D/polyhedral graphic statics.  In graphic statics, there are two diagrams: the form diagram that represents the geometry of the structure, and the force diagram that describes the equilibrium and the magnitude of the internal and external forces in the form.  These 2D diagrams are topologically dual and geometrically dependent. In 3D/polyhedral graphic statics (3DGS), the equilibrium of the external forces or a single node of an equilibrated structure is represented by a closed polyhedron or a polyhedral cell with planar faces. Each face of the force polyhedron is perpendicular to an edge in the form diagram, and the magnitude of the force in the corresponding edge is equal to the area of the face in the force polyhedron. These form and force diagrams are reciprocal. i.e., topologically and geometrically dependent: any change in one diagram results in a change in the other. Moreover, the force diagram represents the equilibrium and magnitude of the internal and external forces geometrically, a property that none of the other form finding tools possess (for further reading, please visit the references section).

PolyFrame is a computational framework that allows the construction and manipulation of reciprocal polyhedrons, currently for compression-only structural form finding. With this tool, a designer can simultaneously design and control the flow of forces in a structural form and drive the optimal structural solutions constrained to certain boundary conditions or specific geometric properties such as edge lengths, surface areas, etc. PolyFrame is based on a polyhedral construction and manipulation environment called PolyFramework. In the upcoming versions of the software, we will include form finding for combined tension and compression and polyhedral truss analysis. 

PolyFrame and PolyFramework are developed by the Polyhedral Structures Laboratory at PennDesign, University of Pennsylvania.

Principal Investigators

Dr. Masoud Akbarzadeh (masouda@upenn.edu), Dr. Andrei Nejur (nejur@upenn.edu)

Software Developers

Dr. Andrei Nejur, Dr. Masoud Akbarzadeh


This work is funded by the National Science Foundation CAREER Award (NSF CAREER-1944691).


PolyFrame, Efficient Computation for 3D Graphic Statics



License Cost:
PolyFrame Beta
Rhino 6 for Win
Rhino 7 for Win
PolyFrame Beta
Rhino 6 for Win
Rhino 7 for Win
PolyFrame Beta
Rhino 6 for Win
Rhino 7 for Win
PolyFrame Beta
Rhino 6 for Win
PolyFrame Manual
Rhino 6 for Win
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