Domical structure and method for its manufacture

An improved domical structure is disclosed built from thirty identical flat isosceles triangular sections of expanded polystyrene which are further divided into two triangular subsections. The division is from either of the two equal sides of the section to the opposite apex which is bisected into two equal angles. This division creates sixty similar yet unidentical flat scalene triangular subsections of equal height as measured from the largest side which are interconnected by means of a spline joining arrangement in a manner that the dividing line of a triangular section never aligns with the dividing line of an adjacent triangular section thus making a stronger more self supporting shell both during and after construction. The structure is covered both on the inside and outside with a fiber reinforced cementitious structural coating.

This invention relates to a domical structure made from a plurality of flat 
triangular sections. 
R. Buckminster Fuller and others (Dome Book II, 1971, by Pacific Domes) 
have described and popularized domes as building structures and described 
various possible geodesic breakdowns of the elements to make such domes. 
The present invention describes an improvement to the inventor's earlier 
U.S. Pat. No. 4,287,690 which utilizes lightweight triangular panels with 
continuous edge tongues and grooves to construct a domical structure. 
In order to make such a structure of substantial size the individual flat 
panels would be too large to be made from a single piece of material. For 
example, readily available material at present comes in eight inch thick 
sheets sixteen feet long by an untrimmed width of fifty inches. Normally, 
this is trimmed to forty-eight inches in width to eliminate the rough 
untrimmed edges. When the flat triangular sections of the prior U.S. Pat. 
No. 4,287,690 are made from two separate triangular subsections the 
dividing line between the subsections are weaker than the undivided 
material. The present invention provides for a domical structure made of 
flat triangular sections which are too large to be made from a single 
piece of available material and are too large for normal handling. The 
invention utilizes triangular sections which have been further divided 
into two unique triangular subsections that are easily handled during 
construction and can be uniquely arranged and joined together in a manner 
to minimize the weakness caused by the division. 
The preferred embodiment is made from sixty of these triangular eight-inch 
thick expanded polystyrene subsections and sixty-nine expanded polystyrene 
splines to construct a geodesic dome with a hemispherical diameter of 
thirty feet and a center height of nineteen feet. This gives a first floor 
space of 500 square feet with up to 500 square feet of optional second 
floor space. The structure is extremely strong, energy efficient and easy 
to construct using an inside and outside skin of one quarter inch thick 
coat of a concrete plaster made from cement, masonry sand, synthetic latex 
and an open weave of fiberglass reinforcement with an additional synthetic 
elastomeric coating on the exterior for additional weatherproofing, 
finish, texture and color. One or more additional coats of material may be 
applied to the interior surface for extra fire resistance. The domical 
structure has three openings in the base which may be framed out with 
conventional wood framing techniques for windows and doors or to join 
multiple domes to each other.

With reference to FIG. 1 there is shown the domical structure 10 of this 
invention exploded into a domical part 11 and framed-in part 12. The 
domical part 11 is made of six pentagonal supersections or building 
modules, three of which are joined at the top to form the top substructure 
and three at the bottom form the base substructure. Each pentagon building 
module is made of five triangular sections and each of these are divided 
into two triangular subsections. With reference to FIG. 1 there can be 
seen the entire pentagon building module 20 as part of the top 
substructure but the remaining two building modules 21 and 22 are hidden 
in FIG. 1 but shown in FIG. 2. 
For convenience of illustration the pentagon building modules are 
identified by their numbers with arrows pointing to the apex of the 
module. 
The three pentagon building modules 20, 21 and 22 form the top substructure 
and the pentagon building modules 23, 24 and 25 form the base 
substructure. The entire module 24 can be seen in FIG. 1 and parts of 
modules 23 and 25 can also be seen. Parts of the three modules 23, 24 and 
25 can be seen in FIG. 2. 
Pentagon building module 20 has been further divided in FIG. 1 into flat 
triangular sections 14, 15, 16, 17 and 18 with each of the sections being 
further subdivided into flat triangular subsections 14a, 14b, 15a, 15b, 
16a, 16b, 17a, 17b, 18a, 18b, respectively. Each of the other five 
pentagon building modules can be similarly divided. 
The framed-in part 12 of FIG. 2 fills the openings between the three 
pentagon building modules forming the base. The framed-in part 12 has a 
wood keyway end plate 14 surrounding the periphery of the structure and 
bolted onto a concrete slab as shown in FIG. 4. Over each of the three 
openings there is a wood header 27 and each of the three openings as shown 
are enclosed by two plywood panels 28 which surround a rectangular 
opening. The opening is adapted to be enclosed either by windows, doors or 
as a connector to other structures to form a cluster of structures. 
With reference to FIG. 3 there is shown a isosceles triangular section 14 
as viewed from the exterior. The two equal sides 29 and 30 are nine feet 
six and one-quarter inches and the long side 31 is ten feet seven and 
one-quarter inches for the thirty foot diameter dome. 
The triangular section 14 is divided into two subsections 14a and 14b. The 
two subsections have a common face of the same length along the dividing 
line 32. The dividing line runs from the apex to a point of one of the 
equal but divided side 30. The point is chosen so that the two triangular 
subsections 14a and 14b each have the same height, which is fifty inches, 
as measured from longest side. This results in triangular subsection 14a 
having a short side of four feet six inches and triangular subsection 14b, 
the larger of the two subsections, having a short side of five feet and 
one-quarter inch. The dividing line 32 bisects the apex into two 28 degree 
angles. 
The dotted line 34 surrounds each of the subsections and depicts a groove 
in the subsection into which a spline is inserted. The two equal sides 29 
and 30 are bevelled inwardly at a 13 degree angle to permit their flush 
joinder with adjacent sections to form the pentagon building module 20. 
The long side 31 is bevelled inwardly at a 9 degree angle so as to permit 
flush joining with adjacent pentagon building modules. 
Both subsection 14a and subsection 14b are cut from 8 inch thick foam 
polystyrene flat billets of fifty inch untrimmed width and sixteen feet 
long. Normally the billets are pretrimmed to eliminate the poor structure 
at the edges to forty-eight inches width. But with the bevels of thirteen 
or nine degrees along the untrimmed edge the bevelling operation trims off 
most of the poor surface leaving a maximum size triangle as shown in FIG. 
3. The surplus foam material is cut into splines three inches thick by six 
inches wide to accommodate the grooves 31 which are at right angles to the 
bevelled edges three inches deep. There is no bevel to the edge along the 
dividing line 32 which is at right angles to the face of the subsections. 
Thus, there are provided a triangular subsection 14b which approximately 
ten feet seven and one-quarter inches long by fifty inches wide and 
triangular subsection 14a which is nine feet six and one-quarter inches 
long by fifty inches wide both of which can be handled readily by hand in 
building the domical structure. The width or height is measured for each 
subsection perpendicular to the long side to its apex. However, there is a 
point of weakness along the dividing line 32 and this is especially a 
point of weakness where the dividing line meets divided side 30 as it has 
a tendency to bend and sag in that vicinity. To strengthen the section, 
rather than further weakening it, it is important to note in FIG. 1 that 
the dividing line 32 meets the adjacent triangular section 15 along an 
undivided side. The undivided side supports the section 14 from sagging 
and bending at the dividing line intersection. 
Other divisions of the triangular flat section are possible but they must 
be done in the manner shown where a dividing line and its intersection in 
a flat section are supported by an undivided side of an adjacent flat 
section or, as a minimum, is not aligned with the dividing line of an 
adjacent section. 
With reference to FIG. 4, there is shown a cross-section of the domical 
structure 10 with the cross-section going through one of the three 
openings and dividing the structure. The foundation is a four inch slab of 
concrete 33 placed on four inches of a compacted stone base. The concrete 
is suitably reinforced with steel mesh and steel rods and is surrounded by 
a concrete foundation 34 which extends below the frost line. The periphery 
of the foundation is surrounded by a one inch thick layer of insulation 35 
which is glued to the concrete and covered over by a coating of a Cemix 
(Trademark) concrete plaster. The Cemix is available from American 
Geodesics, Inc., 1505 Webster Street, Richmond, VA 23220 and is a 
proprietary water acrylic latex modifier which is used by mixing with 
Portland cement and masonry sand. It is usually reinforced with woven 
fiberglass reinforcement. Other water latex and equivalent coatings are 
readily available which bond with the polystyrene foam. 
Bolted to the top of the concrete slab 33 around its periphery is a wood 
keyway and plate 26. This serves as a substitute for the spline to connect 
said triangular sections around the foundation. Likewise above the opening 
there is a wood header 27 and jambs along the sides. The header serves in 
place of a spline to connect with other triangular sections. 
The groove three inches deep surrounding the triangular sections is 
cemented to the wood keyway and plate 26 and likewise to the wood header 
27 as the domical structure is built from the foundation upwards. The 
cement used is an acrylic latex adhesive, contact cement available from 
DAP Inc., Dayton, Ohio 45401 and there are a number of other adhesives 
available to do the same job. The same adhesive is used in all of the 
spline joints. 
It is to be noted that there is a space 37 between the triangular section 
and wood keyway and plate 26. This is filled in by a filler made from cut 
scrap foam or the adhesive. The spline joint 36 is located between the 
sides of each of the triangular subsections where they meet the adjacent 
subsections. The spline is made from the polystyrene foam sheets so as to 
be three inches high, six inches wide and as long as needed for each 
joint. The groove made in the eight inch thick polystyrene foam flat 
triangular subsections is three inches wide and approximately three inches 
deep. 
It is to be noted in FIG. 4 that the cross-section only shows the joints 
between triangular sections and the joints between the triangular 
subsections are omitted but such joints are identical with the exception 
that no bevels are present. 
The method of constructing the domical structure is to first cut the 
appropriate number of triangular subsections and splines from a fifty inch 
unfinished width by eight inch thick by sixteen foot long foam polystyrene 
billet of a density of approximately 1.25 pounds per cubic foot. This 
requires sixty triangular subsections and sixty-nine splines. While 
splines and grooves are used in the preferred embodiment, a tongue and 
groove or similar joint may also be used. 
A concrete slab 33 with a concrete foundation 34 and peripheral insulation 
is prepared and laid down as shown in FIG. 4. Other foundations such as a 
wood deck may also be used. To this foundation and its periphery is bolted 
the base plate including the wood keyway and plate 26. To the base plate 
are attached the plywood panels 28 and the upright jambs on each side of 
the three openings which are joined at their top by wood header 27. Three 
wood keyway and plates 26 have tongues angling outwardly to act as splines 
which are inserted into the grooves of the subsections. Other base pieces 
have tongues perpendicular to the plate and serve as the uprights on both 
sides of the three doorway openings to which the plywood panels 28 are 
attached. The three wood headers 27 which run across the top of the 
openings have tongues angled inwardly to serve as splines for the 
subsections to which they are attached. 
The foam material which is utilized in making the triangular subsections is 
preferably polystyrene with density varying from approximately one to 
three pounds per cubic foot, but other materials and other densities may 
be used. 
The wood base and three ten by nine feet doorway openings forming the 
framed-in part 12 of the domical structure acts as a guide for the proper 
placement of the first row of prefabricated foam panels which have been 
pregrooved after being cut from the slab. Starting at the base the 
triangular subsections are driven onto the spline-like uprights of the 
base by a wooden hammer applying beforehand a suitable adhesive to the 
joint. The structure is gradually built up subsection by subsection by 
joining subsections to each other using splines and adhesive until the 
last panel at the top is to be inserted. The last triangular subsection 
panel has the inside edge of its groove removed so the last panel can be 
simply dropped in place from the exterior. Afterwards the inside groove 
edge is adhesively placed back onto the panel to complete the foam shell. 
Any cracks or openings in the shell are filled in. 
Next an interior cementitious skin 38 is applied approximately one quarter 
inch in thickness using the CEMIX (Trademark) concrete plaster using the 
Cemix latex modifier with a blend of Portland cement and masonry sand. 
This interior coat is applied using a first coat of approximately 
one-eighth inch with conventional plastering techniques. Then overlapping 
sheets of open weave fiberglass fabric of a density of 3.97 OSY is 
imbedded in the first coat. Then a second one eighth inch thick coating of 
the Cemix concrete plaster is applied over the fiberglass reinforcement. 
Other reinforcement material may also be used as a substitute or 
supplement if desired. The interior coat is applied from scaffolding in 
the dome interior. Once the inside coat is set sufficiently the outside 
may be walked on while applying a similar exterior coat 39. The inside 
coat 38 and exterior coat 39 complete the structural integrity of the 
domical structure. 
A synthetic elastomeric coating, a number of which are readily available, 
is finally applied to the exterior for additional weather-proofing, 
finish, texture and color. One or more additional coats of the Cemix blend 
or other materials may be applied to the interior surface for extra fire 
resistance. 
The three doorway openings in the base may be framed out with conventional 
wood framing techniques to whatever size windows and doors desired. They 
can also serve as connection points for custom extensions or multiple dome 
configurations and also serve as load bearing walls for the full or 
partial second floor. Interior walls may be placed wherever desired. 
Skylights and roof windows ma be installed in any of the triangular 
sections as desired. The shell with only the edge groove and splining 
system and accompanying base is strong enough not only to be self 
supporting during construction but also can support the weight of the wet 
reinforced interior plaster and reinforcing material until it cures. By 
applying the interior cementitious skin first and allowing several days 
for it to reach initial cure the still unfinished structure is able to 
support the weight of several people as they then apply the exterior 
cementitious coating 39. 
A residence is currently under construction using two of the domical 
structures connected together with a ducted radiant floor slab to store 
both solar heat and heat given off by a central living room fireplace. One 
dome has a fireplace and an open great room with only a "TV loft" leaving 
the rest of the space open to the nineteen foot tall cathedral ceiling. 
The adjacent dome combines a kitchen, dining room and a half bath on the 
first floor and two bedrooms and a full bath upstairs. 
There is thus provided a domical structure covering the same amount of 
space as a rectangular structure with one third less material. It is of 
roughly spherical shape and is one of the strongest, energy efficient and 
most aesthetically pleasing shapes in nature. The triangular subsections 
and triangular sections are the basis for the geodesic dome construction 
to provide one of the strongest geometric forms. The domical structure is 
a monolithic structure with a continuous interior and exterior coating and 
insulating core. There are no cracks for heat to leak out or air or water 
to leak in. The imbedded fiberglass reinforcement provides extra impact 
tensile and flexual strength. It is applied over both the interior and 
exterior. The spline jointing as described above of the triangular 
subsections simplifies construction and eliminates the need for a 
complicated framing system. The seamless reinforced concrete plaster forms 
a long lasting weather-proof structural coating in a variety of 
maintenance free colors and textures. 
The unique division of the triangular sections into two subsections make 
them easier to handle manually and largely eliminates the problem of 
structural rigidity that would otherwise cause sagging and weakness by 
ending the dividing line of the triangular sections preferably along one 
of the short and equal sides of the isosceles triangle and arranging for 
the dividing line to abut up against the short side of an adjacent 
triangular subsection which has not been divided. The thermal resistance 
of the lightweight foam core panels is R-32+ which provides a structure 
having a minimal heating and cooling cost. 
While a specific structure has been shown, numerous variations can be made 
as to the sizes and arrangements of the panels and still utilize the 
concepts of the invention. The invention can be used for other purposes 
than residential housing and adapted to such uses as required. Therefore 
the foregoing is considered as illustrative only of the principles of the 
invention. Further, numerous modifications and changes will readily occur 
to those skilled in the art, and it is not desired to limit the invention 
to the exact construction and operation shown and described and 
accordingly all suitable modifications and equivalents may be resorted to 
falling within the scope of the invention as claimed herein.