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William Bilyeu


Truncated Hexagonal Block Sculpture: - Early Exploration 01 - Interlocking of Component 02 - Orig. Component Construction 03-04 - Forces and Reactions 05 - Abstracted Geometry 06 - Connections 07 - Local Patterning 08 - Regional Patterning 09-10 - Return to Abstracted Geometry 11 - Case Studies 12-13 - New Component 14 - Component Variations 15 - Component Construction 16 - Forces and Reactions 17 - Component Connections 18 - Local Patterning Connections 19 - Local Patterning 20 - Local Patterning Variations 21 - Local Patterning Construction 22 - Forces and Reactions 23 - Global Connections 24 - Global Patterning 25 - Global Patterning Construction 26 - Final Views 27-28 - Material Variation Analysis 29 - Conclusion 30

EARLY EXPLORATION: Original aim was to create a component through a series of cuts and connections, that will be able to withstand the application of compression force and provide a variety of options for patterning.

1.1 Four sided pyramid with curved base.

In figure 1.1, the curved bottoms limited the possibilities for connections and collapsed when compression force was applied. As a result the component was modified into a basic pyramid with six sides to provide a larger ground surface area, shown in figure 1.2. In an effort to join the interior of the component, the top of the pyramid was removed and reattached at the base, shown in figures 1.3 and 1.4.

1.2 Six sided pyramid, distributes force evenly.

An exploration in material thickness resulted in the discovery that velum increased the resistance of compression forces throughout the component.

1.3 Sketch paper truncated six sided pyramid.


1.4 Vellum, decreased leg rotation.

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INTERLOCKING: In an effort to simplify the joinery in the center of the component, a modification of the component with the alteration of a three piece assemblage that connects at 60 degree angles from one another, secured with a square piece that slides into the bottom to stabilize the legs, shown in figure 2.1. Figure 2.2 shows the exploration of material thickness, which drastically increased the resistance to compression forces and provided possible connection surfaces on the edges of the legs.

2.1 Sixteenth inch chipboard interlocking option.



2.1 Eighth inch chipboard interlocking option.

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COMPONENT CONSTRUCTION: The component is constructed from a template with a very small waste percentage. The first step is to cut along the slit lines and separate all the pieces, as shown in figure 3.2.

3.1 Component template.

3.2 Step one, cut slits and separate squares.


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COMPONENT CONSTRUCTION The second step is to join two of the leg pieces at a sixty degree rotation from each other, shown in figure 4.1. The third step is attaching the third leg still at a sixty degree angle from the others, shown in figure 4.2. The final step is to secure the legs of the component by inserting the squares at the bottom.

4.1 Step two, slide in at 60 degree rotation.



4.2 Step three, slide in remaining piece.

4.3 Step four, slide in squares on the bottom.

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5.1 Compression force applied on top surface.

5.2 The force transfers straight down the center.

Compression forces are applied to the top of the component and there is very little resulting deformation within the component, as shown in figure 5.2. This lack of deformation is due to the forces being directed straight through the center of the component. The component has been proven to support up to the weight of a student, as shown in figure 5.3.

5.3 Component supporting the weight of a student.


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ABSTRACTED GEOMETRY: The abstracted geometry of the component is a truncated hexagonal pyramid, as shown in figure 6.1. The abstracted geometry provides connection surfaces on all of the faces and edges of the component, however the strongest connection will be on a bottom to bottom connection, as shown in figure 6.2. These connections could also happen in a top to top orientation and then connect to the inversely connected pair on a edge to edge connection, as shown in figure 6.3.

6.1 Truncated hexagonal pyramid.

6.2 Bottom and top surfaces distribute forces straight through.

6.3 Ridges between surfaces provide connections.



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CONNECTIONS: Exploration of the abstraction of the component resulted in the wire frame model, shown in figure 7.1, which easily displays the patterning connection locations and options. Figure 7.2 shows the first attempt in creating a connection joint that would be able to provide connections for patterning in multiple directions.

7.1 Abstracted wire frame, shows possible patterning option.


7.2 Multiple direction connection joint.

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LOCAL PATTERNING: The local patterning of the component is a face to face connection either in the top to top or bottom to bottom orientation. These connections are inverses of each other and can be seen in figures 8.2 and 8.4.

8.1 Local top-top surface connection.

8.3 Local bottom-bottom connection.



8.2 Top-top connection, moves forces down.

8.4 Bottom-bottom connection, moves forces down.

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REGIONAL PATTERNING: In the regional scale, the inverse components can be attached in a horizontal manner on a edge to edge connection, as seen in figure 9.1. This connection type can then be applied to multiple components and aggregate out in a maximum of three directions in a plane as well as in a vertical orientation to create depth. 9.1 Horizontal ridge connection.

9.2 Connection doesn’t slip out.

9.3 Connections allow stacking in multiple directions.


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REGIONAL PATTERNING: The second regional patterning option occurs when two locally patterned components are attached in an edge to edge manor, curving inwardly, as shown in figure 10.1. When six of these components are aggregated in the same orientation, they join together to form a hexagon, shown in figure 10.3. 10.1 Angled ridge connection.

10.2 Begins to enclose.

10.3 Joins into a hexagon.



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RETURN TO ABSTRACTED GEOMETRY: With the completion of the midterm presentation, a return to the abstracted geometry of the component was suggested in order to achieve a simpler form in which would achieve complexity in its aggregation. Returning back to this simpler form also allows for stronger connections between components than the original edge to edge connection.

11.1 Abstracted component.


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CASE STUDIES: Along with the simplification of the component, looking to case studies for examples of complex aggregations began. The Voussoir Cloud provided an example of varying components in a manor where the overall form became less dense as it rose up from the ground. This idea of increasing and decreasing density throughout the global aggregation creating a structural relationship is what was taken away.

12.1 Voussoir Cloud, IwamotoScott global form.



12.2 Voussoir Cloud, IwamotoScott component variation.

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CASE STUDIES: The GAUD12 exhibit and the Table Cloth are examples of simple components with complex connectors, in which each connection connects one component to several other components. In these examples, both global forms are being supported by suspension systems, which is a different structural system than the compressive system that the original aim depicts.

13.1 GAUD12: Student Exhibition Pratt Institute, SOFTLAB emphasized connection.


13.2 Table Cloth, Ball Nogues Studio various and emphasized connections.

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NEW COMPONENT: Applying a snap into the ridges of the component was based on the connectors from the previous case study. These snaps help secure the correct angle between the component faces and limit deformation which can occur when compressive forces are applied to any of the component’s faces. The new component which resulted from this addition is also easier to fabricate due to its simplistic fold-up method of assembly.

14.1 Final component, front view.



14.2 Final component, top view.

William Bilyeu

COMPONENT VARIATIONS: Using the idea of component variation which was seen in the first case study, the new component has three varieties which are to reduce the visible load of the global form as well as serve a structural purpose. The most dense component, figure 15.1, is the structural option in which is used in a location of the aggregation where high compression forces are located. The least dense component, figure 15.3 is used at the edges of the aggregation where there are little compressive forces. The medium density component is used to link the other two variations together in a manor that is not shocking on the eye visibly.

15.1 Most dense, structural component.


15.2 Medium dense component.

15.3 Least dense component.

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COMPONENT CONSTRUCTION: The component is constructed in two steps, the first is to cut out the template of the component and the associated connectors. The second step is to fold the component on the score lines and insert the snapping connectors to secure in place, a small amount of glue is added onto the overlapping slits, for added support. 16.2 Component folds on score lines and connectors are inserted.

Cut Line

16.3 Component end tabs are glued to secure geometry in place.

Score Line

16.1 Component template with connectors.



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FORCES AND REACTIONS: The constructed component balances compression forces throughout evenly. You can see this in the minimal resulting displacement from an applied 500 psi compressive force load.

17.1 Component geometry with 500 psi applied.


17.2 Resulting displacement with a deflection scale of 10.

William Bilyeu


COMPONENT CONNECTIONS: The snapping connectors which the component uses are arrowhead shaped so that after they are inserted, they are difficult to remove. The back side of them are set to the angle in which the component faces must stay secured to, preventing deformation when compressive forces are applied.

18.1 Connector shape is designed to snap in place and lock.



18.2 Connectors secure faces of component in place.

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LOCAL PATTERNING CONNECTIONS: Similar to how the component snap connectors secure the faces in place, the local aggregation connection secures the connecting faces of neighboring components so that they do not become disconnected with applied forces.

19.1 Local aggregation adds an additional connector to attach two components together.


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LOCAL PATTERNING: The local aggregation is assembled using the local snapping connectors where ever two component faces align. The resulting local aggregation block is constructed from eight components that are attached on everyother face on the base component, then connected to an equally built half. This local geometry is a threelegged hexagonal ball, similar to a soccer ball, in which it distributes forces evenly.


20.1 Step 1

20.2 Step 2

20.3 Step 3

20.4 Step 4

20.5 Step 5

20.6 Step 6

20.7 Step 7

20.8 Step 8


William Bilyeu

LOCAL PATTERNING VARIATIONS: Keeping the same variation from the single component, the local aggregation blocks have three variations ranging from a light-weight and low density block for the top of the aggregation to a very dense and structural block used in high compression zones.

21.1 Structural variation.


21.2 Regular transitional variation.

21.3 Light-weight variation.

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LOCAL PATTERNING CONSTRUCTION: The only step in constructing the local aggregation blocks is to attach a local snap connector on both sides of a face-face component connection. With the use of these snaps, the local block will be able to withstand compression forces without deforming drastically.

22.1 Local aggregation adds an additional connector to attach two components together.



William Bilyeu


23.1 Variation one with 500 psi compression.

23.2 Variation two with 500 psi compression.

23.3 Variation three with 500 psi compression.

23.4 Variation one resulting displacement.

23.5 Variation two resulting displacement.

23.6 Variation three resulting displacement.


William Bilyeu

When a uniform compression load of 500 psi is applied to the three types of local blocks, a drastic variation in resulting displacement occurs. The most structural and dense block suffers little displacement, but the least structural and dense block gets crushed. This structural analysis further shows that the variation of the components must be applied in the proper locations as to not cause complete failure of the entire aggregation.


GLOBAL CONNECTIONS: The global connection is a simple plate in which is bent and folded in the center, and attached to the surfaces of two component faces when two local aggregation blocks connect.

24.1 Connecting plate secures local blocks together.



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25.1 Step 1

25.2 Step 2

25.3 Step 3

25.4 Step 4

25.5 Step 5

25.6 Step 6

25.7 Step 7

25.8 Step 8

25.9 Step 9

25.10 Step 10

25.11 Step 11

25.12 Step 12

25.13 Step 13

25.14 Step 14

25.15 Step 15

25.16 Step 16


William Bilyeu

The global aggregation of the assembly begins with three local blocks forming a trunk for which will fan out from the center whilst creating a play with the density of the blocks to inform a positive and negative relationship with light and shadow. The completed aggregation includes 111 local blocks, for a total of 888 components.


GLOBAL PATTERNING CONSTRUCTION: The construction of the global aggregation is simple and only requires the addition of the plate connection to the aligning surface between local blocks. The aggregation will likely be assembled from the ground up adding one row at a time.

26.1 Connecting plate secures local blocks together.



William Bilyeu

FINAL VIEWS: The final aggregation of the assembly creates a truncated hexagonal block sculpture, which when viewing from varying perspectives changes the assemblies opacity. This is seen in the elevation comparison of figures 27.2 and 27.3.

27.1 Top view.

27.2 Front elevation.


27.3 Right-side elevation.

William Bilyeu


FINAL VIEWS: With the construction of a scaled global model, an exploration for finding a function for the assembly resulted in an idea for which during the day, the assembly will provide shade, and during the night, the assembly would be illuminated to provide light.

28.1 Scaled vellum model.

28.2 Illumination at night.



28.3 Provides shade during day.

William Bilyeu


29.1 1/8” Plywood

29.2 1/8” Chipboard

29.2 1/8” Acrylic

1/8” x 48” x 96” Sheets.

1/8” x 28” x 44” Sheets.

1/8” x 48” x 96” Sheets.

- $14.57 per sheet - 20 Components per sheet - 45 Sheets needed

- $3.05 per sheet - 4 Components per sheet - 222 Sheets needed

- $139.20 per sheet - 20 Components per sheet - 45 Sheets needed

Total Cost:



Total Cost:


Total Cost:

With the expectation to build the assembly into full scale, a variety of material selections were explored and calculated to figure the overall cost of material for the aggregation. The top three materials are shown here, 1/8” plywood at $655.65, 1/8” Chipboard at $677.10, and 1/8” Acrylic at $6,264.00. With the estimated material cost, the two best options would be either plywood or chipboard.


William Bilyeu


CONCLUSION: With the new component variety and completed global aggregation, the project has solved many of the issues in which it was plagued with during the midterm. However, there are still a few problems which need to be ironed out next semester before the full scale model can be assembled. A definite material selection is the first, with it still remaining a compression resisting structural system, the best material choice options would be rigid with little chance of fracture, this could be accomplished by an engineered wood product or chipboard. The addition or modification of a new global connector may also be needed as to create a stronger connection similar to the snap connections in the component and local scale. The global aggregation is also lacking a strong programmatic use, so the addition of a program is a necessary addition continuing with the evolution next semester.



William Bilyeu

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