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I have run into a bit of a problem creating my 3D model. I started with a single mesh and added additional meshes (all in edit mode) to create my geometric shape. They are all part of the same object, but now I can't figure out how to "carve" my desired shape of this geometric mesh pattern because some of my faces are going to get deleted etc.

Here are pictures of what I have, and what I want to achieve.

enter image description here

enter image description here

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Goodness you have a lot of faces in those objects. Anyway, have you tried extruding your star shape and the performing a boolean operation on the two? – Byte56 Feb 22 '13 at 5:18
I wanted a smooth edge when I sculpt it later on (it is going to be a shuriken). The problem is, I can't extrude the faces because the meshes are overlapping, not joined. I don't know how to join them without destroying the perfect geometric shape. I tried "Removing Doubles" but that resulted in a disfigured mesh blob. – Matt Feb 22 '13 at 16:10
I suggest starting over. That's a crazy number of faces. Start with just the shuriken shape, and use the face tool to add faces to it. Something like this question. – Byte56 Feb 22 '13 at 16:20
One problem with doing it that way, how would I design it using precise geometry? I can't have a, "well that looks about right" model. – Matt Feb 22 '13 at 19:21
You might also want to try modelling a single spike and using array resp. wrap modifier to create the other spikes. If you really need to be precise, I'd recommend Robert Burke's precision modelling guide: – sarahm Feb 28 '13 at 17:36

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