There are lots of excellent 3D modelers on this board. What is the best program to start tinkering with 3D modeling?

I'd start with TinkerCad: https://tinkercad.com/

Very easy to use, free, works in the browser, and most importantly, it always exports a solid model.

This is really important if you plan to 3D print your model.

Hope this helps!

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Epic Gamers Los Angeles Chapter

Hmm, SketchUp is a lot easier and it's free. It does have it's limitations though.

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Bits Blitz - The place to be for all your bits needs!

http://www.shapeways.com/shops/bitsblitz

Sketchup us also easy but doesn't always create solids.

I've used both with 3D printing and had much better results with tinkercad.

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Epic Gamers Los Angeles Chapter

True, but you can fix that easily by uploading it on Netfabb's cloud service.

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Bits Blitz - The place to be for all your bits needs!

http://www.shapeways.com/shops/bitsblitz

+1 for sketchup

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Shapeways store: https://www.shapeways.com/shops/tinywares

Blogging about 6-15mm wargaming: http://www.lead-space.net

Blender!
*if you dare

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I like Moment of Inspiration at www.moi3d.com. Not free, but affordable compared to the fancy programs, and it has a gentle learning curve.

Is anyone aware of a decent 3D programme that runs on iPad?

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There is none that you can use for "real" 3D modelling.

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Shapeways store: https://www.shapeways.com/shops/tinywares

Blogging about 6-15mm wargaming: http://www.lead-space.net

It depends a lot on what you're planning to model, I think; for example, I use Sketchup for my ships, and I find it extremely useful, but I think it would be a nightmare to use to make organic shapes!

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My shapeways shop!

https://www.shapeways.com/shops/Armand

123D Sculpt is a 3D sculpting tool for iPad

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You cant use sketchup on ipad. Also 123sculpt is no use for our hobby really. So if your intention is to create something and to print to use with epic, use computer. I have ipad and I bought all the 3D programs that are available... And now I use computer and sketchup which rocks

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Shapeways store: https://www.shapeways.com/shops/tinywares

Blogging about 6-15mm wargaming: http://www.lead-space.net

You're not going to be able to do anything highly detailed on an iPad

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http://www.troublemakergames.co.uk/
Epic: Hive Development Thread