About: Penrose C4 Cartwheel

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About: Penrose C4 Cartwheel Sponge Permalink

An Entity of Type : owl:Thing, within Data Space : 134.155.108.49:8890 associated with source dataset(s)

This is a placeholder for a Penrose C4 cartwheel. It can be built using the property that if you build a triangular pyramid on top of two connected rods that are spanning an angle of 72°, the top sphere is directly above the point where the sphere of a penrose dart needs to be. So looking from directly above (and ignoring the perspective distortion) this looks like penrose dart. By using two levels one can build a complete penrose tiling. Note that the central rod (grey in the model) is effectively a support rod.

Attributes	Values
rdfs:label	Penrose C4 Cartwheel
rdfs:comment	This is a placeholder for a Penrose C4 cartwheel. It can be built using the property that if you build a triangular pyramid on top of two connected rods that are spanning an angle of 72°, the top sphere is directly above the point where the sphere of a penrose dart needs to be. So looking from directly above (and ignoring the perspective distortion) this looks like penrose dart. By using two levels one can build a complete penrose tiling. Note that the central rod (grey in the model) is effectively a support rod.
Rods	634(xsd:integer)
dcterms:subject	Mathematical Sculpture
PageTitle	Penrose C4 Cartwheel
filename	Penrose C4 model opt 2.jpg
Type	Mathematical
Caption	CAD model of a Geomag Penrose C4 cartwheel
dbkwik:geomag/prop...iPageUsesTemplate	dbkwik:resource/GVJoJNZVdzfd8RbMw3vdAw==
Author	--08-05
Title	Penrose C4 Cartwheel
Spheres	361(xsd:integer)
Triangles	126(xsd:integer)
abstract	This is a placeholder for a Penrose C4 cartwheel. It can be built using the property that if you build a triangular pyramid on top of two connected rods that are spanning an angle of 72°, the top sphere is directly above the point where the sphere of a penrose dart needs to be. So looking from directly above (and ignoring the perspective distortion) this looks like penrose dart. By using two levels one can build a complete penrose tiling. Note that the central rod (grey in the model) is effectively a support rod. There is just one problem. When you put 2 Penrose darts built this way together, the two pyramids cause steric problems. The smallest angle between the rods is about 43°. The solution is to remove some of the rods that clash. Only the penrose darts can be filled with panels (2 triangular). After removing clashing rods only 126 remain.

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