Q-expansions are developed by applying a Style Hierarchy (previously called a Modal Hierarchy) to all Types/Levels in a Principal Typology. The style hierarchy subdivides each Type into 4 and creates Subsidiary Typologies. (See a similar subdivision in Levels of the Root Hierarchy.)

The Style Hierarchy levels do not represent taxonomic elements: they generate a more specialized element from a general element. Formula used are: α, β, γ, δ. The new specialized elements are therefore 28 in number:

There are 8 Style Hierarchies (one for the Root and 7 for the Principal Typologies) and each has different level descriptors. It is not known whether there is a commonality.

Graphic

Formulae

NOTE: ■ = the stem of the formula, which varies according to the taxonomic location of the particular structural hierarchy. It may either be RH- or PH'•-. It is not currently known whether RH'- allows a Q-expansion.

The structures and formulae that exist here are as follows:

Qt:

■Qt1, ■Qt2, ■Qt3, ■Qt4, ■Qt5, ■Qt6, ■Qt7 Each Qt• has the standard cells and properties associated with typologies e.g. TET, dualities. See details.

QH:

■Q1H, ■Q2H, ■Q3H, ■Q4H, ■Q5H, ■Q6H, ■Q7H Each Q•H has the standard cells and properties associated with hierarchies e.g. transitions, oscillating duality. See details.

QC:

■Q1C, ■Q2C, ■QC3, ■QC4, ■QC5, ■QC6, ■QC7 Each Q•C has the standard cells and formulae associated with Spirals. See details.

QHK:

■Q1HK, ■Q2HK, ■Q3HK, ■Q4H4, ■Q5HK, ■Q6HK, ■Q7HK Each Q•HK has the standard cells and formulae associated with Trees. See details.

Q•sHK:

■Q1sHK, ■Q2sHK, ■Q3sHK, ■Q4sHK, ■Q5sHK, ■Q6sHK, ■Q7sHK Each Q•sHK has the standard cells and formulae associated with Trees. See details.