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Sorry, my Google-fu has drawn a blank on this...

Can Stella net a 'ball' shape consisting of a short, pentagonal prism capped at both ends by a truncated pentagonal pyramid ?

So, it has five parallelogram or square faces, ten trapezoidal faces and two pentagonal ends ??

I'd also like to export it as OBJ, so we're probably talking 'Great Stella'...

Thank you.

Yes it can, here's how (you need Great Stella for this)

• Start with a pentagonal prism:
  
• If you want to change the pyramid height before starting, use "Scale->Stretch (Non-Uniform Scale)"
• Select a pentagonal face
• Use "Poly->Augment Polyhedron" (keyboard shortcut: a)
• In the dialog that appears, select these options: Augment using...Prism (everything else can stay as default). You'll see this preview of the augmentation:
  
• Use Ctrl+Right-drag to scale the top of the prism as required:
  
• Use Ctrl+Left-drag if you want to change the height of the augmentation:
  
• When happy, hit Enter to accept the preview as your new model
• Now you can see nets, eg here it is with the 3D unfolding nets:
  

Thank you, thank you.

I have ordered a 'Great Stella'.