1. Create an ICOSAHEDRON, align its center to the origin point.

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2. Create Hexagonal Pattern on one of its flat surface

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3. Copy this hexagonal patterns to the other surface accordingly

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4. Extrude TO POINT these hexagonal patterns to the center point of the Icosahedron (origin point). Open capped.

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5. Create a sphere (start from the origin point) with radius size is SMALLER than the hexagonal 'cones'. Then TRIM the sphere with all of the hexagonal cones.

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6. The hexagonal patterned sphere is done.

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FYI, this kind of model could be easily made within Blender.