Reciprocal star (no ontology)

<div style="display:block; float:right; padding: 8px 8px 0px 8px; margin: 0px 0px 8px 8px; border: 1px solid #888; background-color: #EEE;">http://teamikaria.com/dl/wBtwSfebpkBgk8DAxq07NDy1VUXg_L8oFR7bDwhKIL60L7II.png<p>A '''3M''' reciprocal star with ''k'' = 1.</p></div>

'''Reciprocal stars''' are a set of objects in three dimensions defined by implicit equations. They are so named because their appearance is similar to that of the 2D reciprocal graph, ''y'' = ''kx''<sup>-1</sup>. The implicit equations of reciprocal stars take the form:

''f''(''x'',''y'')''g''(''y'',''z'')''h''(''x'',''z'') = ''k''

== The ten basic reciprocal stars ==
The ''basic reciprocal stars'' are a set of ten specific stars. These are created by using the three [[bracketopic product]]s: sum (''S''), max (''M'') and root-sum-square (''R''). Each possible combination of these to replace the functions ''f'', ''g'' and ''h'' becomes a basic reciprocal star, which are given the following names: '''3S, 3M, 3R, S2M, S2R, M2S, M2R, R2S, R2M and SMR''', where 3''X'' means that all functions are replaced by ''X'', ''X''2''Y'' means that one function is replaced by ''X'' and the other two by ''Y'', and SMR means that all three of the functions ''S'', ''M'' and ''R'' are used.

[[Category:Shapes]]