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There is no exact rotation symmetry, nor axial symmetry in this phyllotactic dome (top). But on any concentric circle on it are knots in Fibonaccian numbers, or doubles of it. The base ring counts 34, the centric ones 8, 5, and 3. You may say that there is a Fibonaccian symmetry. Note the nice transitions between rings.
This dome lacks stability as long as (a) only rods are used, or (b) quadrangles and pentangles are not divided in triangles.

Most of the magnetic models shown in this sequence (bottom) have rings with elements in Fibonacci numbers.