underside of hypar roof


Technology Education & Design

Types of Hyperbolic Paraboloids

Names of Hyperbolic Paraboloids used on this site.

HyPar Ted

4 minute read

This article offers a sample of basic Hyperbolic Paraboloids types that can be used in roofing homes, also it shows basic combinations used together.


Some names are used by others, other HyPars where named after look alike roofs, third type, Tully, named after a person who used this special type as a solution to a vexing issue in drainage. Fourth type named after bees..

Really, bees, got the idea for a 6 sided roof after a friend gave me a bee hive formation information.


First type is the single shell like the top image. Which would be used like this for solar energy collection. In the way we use HyPars, this would be called on its side. the wall type is similar to top image but the shell would be rotated upright. The top point of the wall HyPar is vertical, and the bottom point is horizontal. The wall type fits in the triangle opening of the gable and used to enclose the space.

The wall type is used in the site logo. wall is like on of the elements of the next type.


is Also like the wall type vertical point on high center and lower side horizontal. But is made of 4 identical single shell, combined to support each other and used as a square unit.


Hat the is the most common type made and reasons for it is numerous. With the funnel like top used for fire and smoke draft, cooling, etc. The base is horizontal and act like headers for doors and windows. Only thing, don’t care for the looks. My favorite is the next type.


My favorite shape, much more usable attic space over hat, better headroom than a stick built gable with arches as diagonals. Not as simple to built as the hat. Usually built elevated on posts and needs a center post during construction.


image is somewhat misleading the legs and roof peak are lined up and plumed. The next one they are not lined up.


A fun named HyPar, same role and construction details as gable the roof ridge is elongated, over gable


The home I designed for myself as my first to build was a batwing over a gable, was shared with other engineers as the least costly HyPar building idea. Ended up used as disaster recovery in the Philippines. Will share more details on the construction ideals in a future post, warning will be long!


This is like gable roof but the roof has a slight angle to it. That is for more headroom and to reduce the thrust downward at the center. Not used much.



Found this HyPar on a building at a college. Tracked down the retired engineer/inventor and called him out of the blue. Nice guy, talked for hours. When joining gables, drainage problem can occur. This is a true single HyPar, but I model it as a hat over the valley of two gables. Because that is the way I would likely build one.



Is a six sided HyPar made of three single identical shells as a unique creation. Got the idea from the way bees start the hive. The hive cells are jointed in the back. Back to back with offset that creates the six sided cells of the hive bay. This should be the least costly in terms of material like a hat type. But one less shell is needed. The clear span would be limited and less than 30 ft. ballpark estimate around 24-25 ft. Someday I may put pencil to paper and figure it exactly. Being a hexagon, it would mesh nicely. Once had a Y shaped house project that used hexagon with gables. House became too large to fit my lot, so idea dropped. looked nice.


Is a mathematical method verses a set HyPar, used to joint different sized Gable roofs and different elevations. They can be more complex then needed, if the hypar gables are only spaced a few feet apart. Solution to small gaps is to extend the lower gable ridge and frame it normally. however if less the distance than half the smaller gable, U-Fit can provide a HyPar solution.


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