I recently had a short trip down to Melbourne and took a few pictures of the Arts Centre Spire which was constructed in the late 1970s.
Conceptually, the spire is a sculpture which was intended to indicate the location of something special located under the tall, tapering open lattice structure.
The "upper spire" is from bolted steel tubes with a geometry utilizing tetrahedrons so as to reduce the number of members meeting at a joint. Four joints are at each higher level and these four are rotated by 45 degrees in plan from those at the adjacent levels.
The "lower spire" is constructed using annodized Aluminium tubes and the Triodetic connector. There are four complete hypars with sixteen divisions on each side. In addition there are eight "truncated hypars" with the outer edges being formed with a double layer for stiffening of the free edge. The overall effect required by the Architect (Sir Roy Grounds) was that it would resemble the skirt or Tutu of a ballerina.