Question and Scope of Answer
The question is about metaphors and semantics relating to the carbon stoichiometry of the reactions producing dihydroxyacetone phosphate from carbon dioxide. I have decided to provide a clarification of the carbon stoichiometry, ignoring hydrogen and oxygen stoichiometry (even though I find the reduction and energetics more interesting). The answer depends on what you consider the metaphor “turn of the cycle” means in relation to this sequence of reactions, and is of little interest or importance.
The so-called dark reactions of photosynthesis produce one molecule of glucose (hexose) from six molecules of carbon dioxide in a two step process.
6 CO2 → 1 C6H12O6
In the first step — the so-called Calvin Cycle — three molecules of CO2 are converted to the triose, dihydroxyacetone phosphate (DHAP).
3 CO2 → 1 C3H7O3PO32–
In the second step, similar to the final part of gluconeogenesis, two DHAP molecules are converted to glucose.
2 C3H7O3PO32– → 1 C6H12O6
The reason the reactions of the Calvin Cycle are considered a metabolic cycle is that one of the intermediates, the pentose ribulose 1,5-bisphosphate (RuBP), is consumed by reaction with CO2 to give two molecules of triose:
1 ribulose 1,5-bisphosphate + 1 CO2 → 2 3-phosphoglycerate
The problem with the epithet cycle in this case is that it differs from the tricarboxylic and urea cycles where a single molecule enters the cycle and is converted to a molecule(s) leaving the cycle in a single series of reactions regenerating the molecule with which the input molecule first reacted. In the Calvin Cycle, the initial reaction between RuBP and CO2 has to occur three times for the stoichiometric production of one molecule of the triose, DHAP.
Many diagrams that represent the series of reactions as a cycle tend to be stoichiometrically incorrect (or more charitably, ignore carbon stoichiometry to emphasize energetics etc.), rendering the metaphorical expression “turn” of the cycle almost meanless. This is unfortunately the case for the diagrams in two other answers — one molecule of RuBP and one molecule of carbon dioxide clearly cannot generate one molecule of triose DHAP and regenerate the RuBP.
The diagram below from Berg et al. is stoichiometric as it considers the total number of molecules to produce one of DHAP. (The three arrows to the product, Ribulose 5-P, imply three molecules are produced.) I have modified the diagram by de-emphasizing other aspects of the reactions than inputs and outputs.
If you consider (as the anonymous source in the question and many others do) that each time one molecule of RuBP reacts with one molecule of CO2 a “turn of a cycle” is initiated, then six “turns” (or “rounds” à la Berg) are required to produce one molecule of glucose; if you consider each series of reactions that produces one molecule of the triose, DHAP, represents one “turn of a cycle” then two “turns” are required. I personally would avoid the metaphor, state what happens, and concentrate on the more interesting aspects of the process, which are the energetics and reductions using the products of the light reaction.