The nature of celestial cube-based shelter together with the cubodal wheel fusion poses the potential for 2 cross gables of differing slopes for any such house built in temperate zones between 30° and 60° (except at 45° where both gables slope at about 35°).
From that middle latitude, the difference between the gables increases – along with the CBS host roofs – until at 60° the polar gable reaches 90° to essentially vanish and the 30° gable settles at about 19° according to the fusion formula.
Φ = ArcSine [ (√3/3) TanΔ ]
Beyond 30° and 60° latitudes – in subtropical, tropical, arctic and subarctic realms – only one CBS roof is receptive to the fused gables – except at the poles and equator where any fusion whatsoever is precluded.
Such restricted variance coupled with the varied directions of road access gives transporter accommodation the potential for being a convoluted undertaking. Fortunately, however, there are options available that are attuned to code geometry and philosophy.
The simplest option pertains to the steeper fused gables – the steeper the more applicable. In this option the 2 half wings are separated such that the ridge becomes a 2-dimensional flat plane. In fusing to the roof’s prime cube projection according to the fusion formula, such a plane will be flat relative to the local horizontal shown by a level. To attain water drainage this plane can be tilted slightly according to the co-cube projection correction.
At this point, it should be stated that the steeper fused gable need not be for transporter housing. The gable can also be used for vents, windows, or bracing for vertical sun-blocking planes. If separated semi spherical skylights atop the resulting flat roofs are perfectly consistent with code geometry.
Another option applies to both shallow and steep gables and is a bit more complex but offers interesting configurations. Hybrid transporter housing combines the annexation approach with one gable slope.
With the hybrid roof, the annexation extends horizontally beyond the confines of the CBS roof such that its ridge is matched by that of the half gable. This configuration of course poses a corner approach to transporter housing.
The hybrid roof enriches the base CBS style with a combination of universal and variable elements. But because a certain complexity is also introduced, the code lays down rules for their implementation to avoid clutter and confusion.
1) an annexation can only extend past one CBS roof (north or south) so as not to obscure or undermine CBS expression of the juxtaposed celestial cube projections.
To construct hybrids using both gable angles (in temperate latitudes) they must be done separately on opposing (east and west corners).
2) separate (full) fused gables and annexations are not allowed on the same structure unless the 2 modes are informed by a hybrid roof.
With a particular sloped hybrid, either the annexation or the corresponding fusion or both may be constructed.
3) only full fused gables are allowed on mirror roofs, i.e., no annexations or hybrids. The reason for this is to avoid obscuring expression of the CBS celestially projected cubes. Mirror roofs already provide sufficient flexibility.
Such fusions are exempt from the rule requiring hybrids to be present for them and separate annexations on the same structure. If a hybrid is used, it must not be on the same side as the mirror roof to avoid confusing or obscuring CBS expression.
Again, the options and their rules are intended to afford variegated flexibility for particular circumstances while retaining intra-latitude identity and inter-latitude code integrity; and they lend the code’s CBS style – otherwise known as Humble Cosmic Architecture – more well rounded roundedness and pose a richer gem without diminishing its unique essence.