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I am trying to make a model of Richard Hammond's crash helmet from The Great Escapists, but I need to slightly curve a cuboid around both sides. this is what I am trying to create:

and the blender model currently: Side front Crash Helmet

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Wouldn't deleting a few faces from a Mirrored, Solidified, Subdivided hemisphere, or half round-cube, make an easier starting point than caving in the front of a full sphere?

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Then duplicate some faces to new objects, and Solidify those the other way..

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You can always randomise it later, maybe sculpt with a cloth brush..

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First off, amazing photo! :) But to give you some direction...

A very simple way to achieve this is to create some planes around your sphere, shrinkwrap them to your sphere, then add some thickness. Let me explain...

Begin with a plane, scale it to the correct size and be sure to apply the scale (CTRL-A -> Scale) I have used an array modifier with an empty as the offset object to get the rotation, this is a simple technique, see here: How to make a circular array using offset object as center?

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Next, you'll need some geometry to work with, so add a Subdivision Surface modifier and set it to Simple

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Then, use the Shrinkwrap modifier to tell the planes to "wrap" onto the surface of your sphere, set up like this:

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Finally, add some thickness to your planes with a Solidify modifier

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You should be able to adapt this technique and play with the settings to get your desired result. Happy Blending! :)

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