Getting Off
the Rectangular
Grid
Tessellated ceiling and wall panels
can be both beautiful and practical
by Nancy Mercolino, Les Eisner,
and Michael Chusid, RA, FCSI
Photo courtesy Ceilings Plus
When it comes to Wall and
ceiling finishes, patterns
based on triangles, pentagons,
hexagons, trapezoids, and
other polygons have become
economically feasible. these
new shapes provide alternatives
to the square and rectangular
grids that dominated so much
of 20th century design.
The use of tessellated surfaces appears to
be a growing trend in contemporary
architectural design. ‘Tessellation’ is the
geometric term for dividing a surface into
polygons (i.e. multi-sided shapes). The
term comes from the Latin ‘tessellare,’
meaning ‘to pave with tiles.’
While tessellated tile designs can be
seen in recently constructed façades, floor
finishes, and skylights, this article focuses
on their use for ceiling and interior wall
panel systems.
A project currently under construction
demonstrates the architectural potential of
tessellations. The main concourse of the
New Doha International Airport (NDIA) in
Qatar, designed by HOK, has a wide-span,
undulating ceiling vault. Its ceiling is
assembled with triangular panels with edges
as long as 1.3 m (4 ft). To better match the
large scale of the concourse, the triangles
are overlain with a rhombic pattern created
by using wider joint spacing around clusters
of eight triangular panels. A third visual
element introduces rhythm by placing
trapezoidal openings beneath skylights that
allow filtered light to cast dappled shadows
onto the floor below.
All these geometric elements are projected
onto curved surfaces sweeping beyond the
glass walls in order to create overhanging
84 the construction specifier | May 2010
Exciting new designs are now possible. The Great Hall of the British Museum has
a tessellated skylight formed by triangles projected onto a curved surface.
Photo © Lindsay Watt
soffits that must resist fluctuations in air
pressure due to strong winds blowing off
the Persian Gulf. In addition to meeting
aesthetic considerations, the aluminum
panels had to:
• be lightweight to minimize loads on
the structure’s long spans;
• provide a high noise reduction
coefficient (NRC) to compensate for
the hard floor surfaces and glazing;
• integrate with lighting, ventilation,
and other building services;
• offer access to above-ceiling HVAC
equipment for commissioning and
servicing; and
• address rigorous sustainable
construction goals.
Form follows technology
Tessellations have been used as decorative
architectural motifs since antiquity,
featured in various flooring designs and
ornaments. In every epoch, architectural
motifs have related to the design and
fabrication technologies in use. In eras
of manual craftsmanship, for example,
elegant tessellations could be laid out
using simple tools such as a straightedge
and compass.
In the Industrial Age, the production
line shaped modern architecture. Ribbons
of material—whether glass, ceramic,
metal, wood, or mineral fiber—moved
down the line to cut-off mechanisms that
produced rectangular sheets or panels.
These right-angled building components
were compatible with the drafting tools
epitomizing the era—the sliding parallel
rule and right-angled triangle.
While non-orthogonal examples can
be cited—such as Frank Lloyd Wright’s
experiments with hexagonal modules in
his Usonian houses and Buckminster
Fuller’s geodesic and Dymaxion projects
—rectangles have been the dominant
planning module of the architectural
era drawing to a close. This is nowhere
more apparent than in the nearly
ubiquitous use of the 610 x 1120-mm
(24 x 48-in.) lay-in grid ceiling.
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A close-up showing differently sized reveals and
precise location of perforations. Panels are made
to tolerances measured in thousandths of an inch.
Photo courtesy Ceilings Plus
Various tessellated designs can be used for floors, walls, and skylights.
Photo © Lindsay Wat
The view of the New Doha International Airport ceiling shows how triangular panels
are grouped to form large rhombic pattern more in scale with the large, vaulted
terminal. Parallelograms indicate locations of skylights. The ceiling is being made
with lightweight, perforated aluminum panels with a light-reflective finish.
Image courtesy Ceilings Plus
86  the construction specifier | May 2010
In the architectural era now dawning, new
technologies are redefining what is practical to
build. Computer-aided design (CAD) and
building information modeling (BIM) require
only a modicum of additional computing power
to define curved and tessellated shapes instead of
orthogonal shapes. Innovative designers can now
write algorithms based on building-program
requirements—such as access to sunlight or
audience sightlines—and then use computational
analysis to suggest ‘generative designs’ not
constrained by historical building forms.
Increasingly, there is little or no rise in cost to
fabricate the digitally created shapes. Acoustical
panels, for example, can now be mass-customized
using computer numerically-controlled (CNC)
machinery that requires less than a minute to
convert aluminum or wood-veneered metal
into ready-to-use ceiling or wall panels. Each
panel is individually trimmed to the required
configuration, perforated for acoustical control,
notched to accept installation hardware and
lighting fixtures, and then folded to create
stiffened edges.1
The machinery does not ‘care’ what shapes are
required. It is capable of producing components
to a precision measured in thousandths of an
inch, which allows even the most complex
Tessellations have been used as decorative architectural motifs since antiquity, featured
in flooring designs and ornaments.
Most tessellations can be altered by elongation or skewing. Regular hexagons can be deformed by changing the parallel edge lengths,
while a pattern of squares can be skewed to create a field of rhombi.
Images courtesy Ceilings Plus
patterns to be prefabricated to fit precisely in the field. Even
construction layout has gone digital with lasers and jobsite
robots. Moreover, new technologies allow the use of an array
of metal, painted, and wood finishes.
system; these springs hold the panels securely in place
while still allowing individual ones to be easily removed
and reinstalled for above-ceiling access. For exterior
panels, cam locks can be added to resist wind loads.
Tessellar geometry
The building blocks of tessellations are multi-sided shapes
called polygons. In ‘regular’ polygons (e.g. equilateral triangles,
squares, pentagons, hexagons, and octagons), all the edges are
the same length, and all the angles between adjacent edges are
equal. There are three ‘regular’ tessellations that can fill a
surface with just a single type of regular polygon—equilateral
triangles, squares, and regular hexagons.
There are also eight ‘semi-regular’ tessellations in which two
or more types of regular polygons can be arranged so the
configuration of polygons meeting at each vertex is the same.
Further, there are 20 ‘demi-regular’ tessellations that are more
complex, but still formable with regular polygons.
Many of these tessellations can be altered by elongation or
skewing. For example, a tessellation of regular hexagons can be
deformed by changing the parallel edge lengths, while a pattern
of squares can be skewed to create a field of rhombi.
Beyond these, are the tessellations composed of ‘irregular’
polygons including non-equilateral triangles, quadrilaterals
(e.g. rhombi and trapezoids), and polygons with non-uniform
edge lengths.
While the number of tessellation patterns is practically
unlimited, architectural applications are typically constrained
by construction practicalities. For example, the most common
installation method for tessellated ceiling panels employ
torsion springs that clip the panels to a concealed suspension
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Wall panels are typically set into slotted hat
channels or onto Z-clips. It is the most
economical to select a tessellation that can be
superimposed onto parallel or other regularly
spaced suspension members; more complex
suspension systems will slow construction by
requiring rigorous layout and assembly.
Layouts needing suspension systems with
radial or other symmetries are also possible.
Ceiling suspension systems should comply
with standards applicable to a project, such as:
• ASTM C 635, Standard Specification for the
Manufacture, Performance, and Testing of
Metal Suspension Systems for Acoustical Tile
and Lay-in Panel Ceilings;
• ASTM C 636, Standard Practice for
Installation of Metal Ceiling Suspension
Systems for Acoustical Tile and Lay-in
Panels; and
• ASTM E 580, Standard Specification Practice
for Installation of Ceiling Suspension Systems
for Acoustical Tile and Lay-in Panels in Areas
Subject to Earthquake Ground Motions.
Facetted geometry in this ceiling, rising above the Tompkins
Community College (Dryden, New York) repeats polygonal forms
created by the structural cross bracing.
Photo courtesy Ceilings Plus
Advanced design options
Once a basic tessellation pattern has been
determined, it can be embellished in a
number of ways. For example, the edges of
adjacent panels may be of different heights so
panel faces lay in different planes. To create
even more pronounced facets, the panel faces
themselves can also contain folds.
Tesselations at
While this wall in the Museum of Modern Art (Loda, Poland) shows a great
variety of shadows and highlights, it consists of just a single k-dron-shaped panel
type. Alternating rows are offset and panels are individually rotated to create
visual interest. The facets also help break up standing sound waves for improved
acoustics in performance spaces.
Photo © Janusz Kapusta
88  the construction specifier | May 2010
Co-authors Nancy Mercolino and
Michael Chusid, RA, FCSI, will delve
deeper into the subject of ceilings at
CONSTRUCT2010 in Philadelphia.
In a session on May 11 entitled,
“Taking Ceilings Off the Grid,” they
will explore how modern metal and
wood assemblies can simultaneously
meet goals for sustainable and aesthetic
design. Topics include building
information modeling (BIM), product
shapes and dimensions, and green
aspects like recycled content materials
and simplified building commissioning.
For more information on the event,
cs
see page 32.
The primary function of perforations
is to enable panels to absorb sound,
allowing noise reduction coefficients as
substantial as NRC = 0.95. However,
their locations are individually
controlled to allow them to function
as pixels in a graphic design. Many
playful visual devices can be employed
as a result. For example, a circular
motif can be superimposed over the
intersection of six triangular panels,
which allows soft curves to play
counterpoint to acute angles. Where
perforations are not a desirable visual
element, using micro-perforations all
but invisible when viewed from the
normal ceiling heights can still provide
noise reduction.
Specifying panels with different
colors or finishes creates additional
effects. The interplay between exposed
metal panels and wood veneered ones
can be especially dramatic, creating
visual tension between smoothness
and grain, and cool and warm—in
some cases, this can create the illusion
of three-dimensionality.
Rotation of polygons creates another
set of design opportunities. For
example, the wall shown in is
composed of a single polyhedral
form—the k-dron, a geometric shape
discovered by architect Janusz
Kapusta.2 Each k-dron panel has a
square, fourfold rotary symmetry.
Rotating adjacent panels allows a
single module to be assembled into
combinations that capture light and
shadow in endless ways and can be
used to diffuse sound reflections.
Curved surfaces can also be
tessellated. In a manner similar to that
used in finite element analysis, they
can be approximated by using flat
polygons to create facetted surfaces.
Alternatively, panels themselves can be
given curvature, and then assembled
into spherical or other curved surfaces.
sprinklers, and other fixtures integrated into a complete ceiling
or wall system. One approach is to locate fixtures in gaps
between panels or in voids created by omitting panels at regular
intervals. However, precision manufacturing can also create cutouts where fixtures can penetrate a panel.
Special attention must be paid to the intersection of tessellated
surfaces with adjoining construction—for example, a ceiling
adjoining a flat wall. One approach is to hold the ceiling away
from the wall to allow the full ceiling panels to form a ‘floating’
edge. Alternatively, many tessellated patterns can be trimmed to
neatly fit into a right-angled corner of a room. Another option is
Practically speaking
Tessellated panels must still be compatible
with lighting fixtures, air diffusers, fire
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Tessellated panels must still be compatible with lighting fixtures, air diffusers,
fire sprinklers, and other fixtures integrated into a complete ceiling or wall system.
to blur the distinction between walls and
ceilings and allow a tessellation to wrap
around corners and transitions.
With off-the-shelf acoustical ceiling panels,
off-the-shelf details can be used. However,
tessellated systems are produced through
mass-customization, and collaboration with a
fabricator throughout the design process can
help ensure project success.
Having a fully coordinated set of shop and
installation drawings is critical, either as part
of a BIM or as 2-D drawings, since each
unique component in an installation has
to be marked and individually located for
installation. Specification of a mockup is also
recommended to verify design intent and
to resolve coordination issues before the rest
of the panels are fabricated.
Tessellated panels around a polygonal window are mocked-up for the façade
of Ravensbourne College in London, England.
Photo courtesy FOA
»
Shape of ceilings to come
While tessellation is an ancient art, new
possibilities are still being discovered. For
example, Penrose tessellations that form
quasi-crystalline patterns were not defined
Additional Information
Author
Nancy Mercolino is president of Ceilings Plus, a producer of
specialty ceiling and wall systems. She can be contacted via
www.ceilingsplus.com.
Les Eisner is a structural engineer. As senior engineer at
Ceilings Plus, he provides customer service to help designers
translate their vision into practical solutions. He can be
reached at leseisner@ceilingsplus.com.
Michael Chusid, RA, FCSI, is president of Chusid Associates,
a technical and marketing consultant to building product
manufacturers. He can be contacted online by visiting
www.buildingproductmarketing.com.
Abstract
The use of non-orthogonal angles is a major trend in
contemporary design, made possible by advances in CAD
and the latest in building information modeling (BIM)-driven
equipment. This article examines tessellations (i.e. tiling of
a plane with polygons), discussing which patterns are most
90  the construction specifier | May 2010
practical from an architectural standpoint, and explains how
ceilings and wall façades can be designed and manufactured
off the ‘square’ grid.
MasterFormat No.
01 71 23.13–Construction Layout
05 58 00–Formed Metal Fabrications
06 42 99–Wood Paneling
09 50 00–Acoustical Ceilings
09 53 00–Acoustical Ceiling Suspension Assemblies
09 54 00–Specialty Ceilings
UniFormat No.
C3010–Wall Finishes
C3030–Ceiling Finishes
Key Words
Divisions 05, 06, 09
Acoustics
Ceilings
Tessellations
Wall façades
until the 1970s. That same decade also brought the
‘Café Wall Illusion,’ which causes parallel lines to
appear to converge and diverge .
Rectangular fluorescent light troffers impose
pernicious constraints on the creative possibilities
of reflected ceiling plans. As light-emitting diodes
(LEDs) approach an affordability tipping point,
many industry prognosticators expect new
illumination paradigms to emerge.
An amazing variety of ceiling and wall systems
have been built during the reign of the straightedge
and compass. With the speed of digital design
and fabrication, we can expect to be amazed by
the new forms still yet to be created in the next
cs
few years.
Notes
1
For more background, see the author’s previous
article, “Metal and Wood Ceiling Systems,” in the
April 2008 issue of The Construction Specifier. Visit
www.constructionspecifier.com and select ‘Archives.’
2
Patented in 1987, the k-dron is an 11-sided
spatial form with unique optical, acoustical, and
structural properties. For more information, visit
www.k-dron.com.
A sphere or other curved surface can also be tessellated. Panels laid out
along longitude and meridian lines are shown in this view of the underside
of the New Hayden Planetarium at the Rose Center for Earth and Space,
Museum of Natural History, New York City. The planetarium is inside a 27-m
(87-ft) diameter sphere clad. It is clad with metal panels with over 5 million
perforations to help control noise.
Photo courtesy Ceilings Plus
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