"Tilted Perpendicular to the Gutter Platforms" have the center seam out of parallel to the gutter, similar to a "Sloped Tent Fold".
With careful design, Platforms can be Compounded. They can vary their pitch along their width, corrugating them by making customized Support Arms and extra folds on the Platform; an extension of the Parallel, Concave, Convex and Tilted concepts.
Platforms can also be Multi-Layered one atop the other in a similar approach to Multi-Layer Scenery Flats.
Finally, they can have enclosed ends, although not in the same manner as Tent Folds.
An Uneven Tent Fold can be used as the basis for an Offset Fixed Parallel Platform. This will shift the seam of the Platform out of perpendicularity from the Gutter, which can be handy in placing a platform off-center. If used, be sure to derive the length and pitch of the Outer Support Arms from their uniquely sloped sides of the Uneven Tent.
As with a Sloped Scenery Flat, Sloped Platforms have their outer Support Arms pitched at an angle radiating from a point on the Gutter, determined by the pitch of the platform.
A variation of the Parallel, Concave, Convex and Tilted Platforms is the Compound Platform. Instead of simply having two halves of a platform divided by the gutter, it can have as many plane changes as desired on each side of the gutter.
The method of calculating exactly what lengths the Support Arms need to be and where they are located on the spread is elegant but not obvious. It is based upon the process of "Bisecting a Given Line Segment".
There are two ways to build platforms on top of one-another. One is to simply repeat all of the steps in making a platform by making new "Z"s, etc. and attaching them to the platform below as though the lower platform is a spread. This introduces more fold resistance and bulk, but allows each layer to be a different style of platform; in turn, allowing complex structures to be designed. Structurally, designs are more rigid when upper Support Arms are in line with lower ones. This carries the load down to the Spread, minimizing stress on lower platform surfaces.
The other method is to employ Triple-Layer Support Arms, and Slots cut in the platforms (see the "Scenery Flats" page, specifically "Multi-Layer Scenery Flats"). This allows for less resistance, and less fold layering.
Triple-Layer Support Arms maintain rigidity along their length, so it is possible to continue the arm up through the Platform to become a free-standing vertical element in the pop-up design; examples being candles on a cake, figures in a scene, etc.
On Parallel Platforms, Closed Ends are attached to the Support Arms. They do not function in the same manner as Closed Tent Folds (which are V-Folds). Instead, they are in themselves essentially Tent Folds. This is because the Closed Ends are hinged off of opposing Support Arms, which maintain parallelism while opening and closing the spread. Therefore, the hinged Closed Ends come together like a tent.
Similar to the Closed Ends of a Tent Fold, Closed Ends of Platforms will not pull completely flat due to hinge spring tension. Also, the box-like forms created by this method must have folds where necessary to shut the spread completely flat.
Because of the way that Platforms fold closed, it is only possible to fold the Closed Ends outward, away from the Platform. So the length of the overall Platform - in the direction of the gutter - combined with the the folded width of both Closed Ends, must be no more than the height of the spread, or parts of the Closed Ends will stick out of the book. Similarly, the folded Platform Width must not exceed that of the folded Spread.
