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Noble Faceted Snub Cube — zdjęcie 1

Noble Faceted Snub Cube

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A polyhdron characterized by identical (but non-regular) intersecting faces and identical vertices.

Ocena
0 / 5
Polubienia
3
Pobrania
20
Wydruki
0
Wyświetlenia
66
Oceny
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Informacje o modelu

Źródło
Printables
Kategoria
Math
Licencja
Creative Commons — Attribution

I came across this polyhedron on the Numberphile video here (at about 14 min):

It was first created by Robert Webb.  Here are some facts about the solid:

  • It is created by connecting the vertices of a Snub Cube in a different way (refaceting), using a self-intersecting pentagon (a sort of 'fish' shape)

  • The faces themselves intersect each other, which creates additional interior edges and corners. These edges divide each pentagonal face exposing 3 polygons

  • There are 24 pentagon faces, exposing 24 irregular pentagons and 48 triangles, 24 each of two different triangular shapes

  • It has the rotational symmetry of a cube/octohedron, but not mirror symmetry, being derived from a 'snub' cube

  • It has chirality, or 'handedness', meaning it differes from its mirror image (print them both!)

Regarding this model:

  • I made this largely to challenge myself in Solidworks and I like the appearance.

  • I printed it so the intesecting edges that make an 'X' rested on the build plate, and this works well.  Since its such a small surface, I added a brim after a failed attempt that detached from the bed after about 30% complete.  I may have succeeded if I washed the build plate and tried again.  YMMV

  • When oriented as described above, the overhangs are just under 60 degrees, which printed perfectly without supports on my Core One printer.  For reference, I used the .15 mm 'balanced' profile with 12% gyroid infill.

  • The included model has 40 mm edges and took about 4 hours to print.

  • It's 91.4 mm in each direction between the 'cube' faces.  Rescale as you see fit

  • I would love to color the faces as shown in the video, but I don't have a multi-color printer yet.  I should have the INDX upgrade soon and I'll reprint when I have it