A thin cylinder buckled by uniform pressure from above develops a symmetric pattern of dimples corresponding to a finite subgroup of its original infinite rotation group, preserving most structure.

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

• Inserting a diamond-shaped compression piece in the lily reduced bending and shear through upper portion via compression preventing internal torquefinding0.755
  Unexpected structural action of a decorative element improved behavior.
• Breaking the infinite symmetry group of a rotating galactic disk produces the simplest consistent subgroup — a two-armed spiral — as the dominant emergent form in M51 and computer simulations.finding0.752
  Mechanistic finding illustrating how the principle of unfolding wholeness operates in galaxy formation through symmetry-group reduction
• In a controlled geometric comparison, subdividing a rectangle asymmetrically with a thin band of space between the four resulting rooms produces a more profound form — with more levels of scale, boundaries, and centers — than simply cutting it into four equal parts.finding0.748
  The geometric demonstration that asymmetrical subdivision with boundary bands creates more living structure
• Shapes have been found, which, within the scheme of unfolding, are able to express the deepest feeling directly.claim0.746
  Author's assessment that the discovered geometries can carry profound feeling.
• the relative harmony or 'life' of a given building may be understood directly from the internal cohesion of the structure... without reference to opinion, prejudice or philosophy, merely as a consequence of the wholeness which exists.quote0.744
  Strong claim that life/beauty is an objective property of the wholeness structure.
• The profound wholeness of living structure, almost every time it has been done most profoundly, has been done in a mystical‑religious context.claim0.742
  A sweeping historical observation that grounds the claim that mystical context is a near‑universal condition for the highest living structure.
• The act of division, creating upper and lower zones, determining proportions of what lies below and what lies above, makes an intervention in the potential field that is as profound as any other act of creation.claim0.742
  Raises spatial division to a foundational creative gesture.
• The relationship of the new volume to the existing structure is almost like a molecular lock-and-key relationship.claim0.740
  The fit is highly complex, very specific, and definite, analogous to protein-ligand binding.