Daily Cubic Zones
Riding home from work on a motorcycle 20 years ago, the wheels below me squealed on pavement and clouds above stood still. Wind rushed my chest and arms, telling me I was headed home now. My workplace was behind. Two left turns and three right turns took me home. Yes, I was in one of my “cubic zones”.
Safe in my 40 miles per hour cubic zone, it was the weekend! My cubic zone traveled with me. Spinning wheels kept gravity from pulling me down onto pavement. Up was an eternity of sky. Facing to the front took me home; back was the way from work. Extend the right arm before turning right; extend left to turn left.
Down, up, front, back, right, and left – all defined orthogonal directions in my cubic zone’s personal coordinate system. As directional vectors, these were each normal to one of 6 faces of my 40 miles per hour cube (below).
I had just left my daily safe cubic zone – my work cubicle in my office building. It was safe and uniformly packed with cubicles in a carefully detailed grid on a square floor plan in my cubic office building. Cubicle space, carpet patterns, bookshelves with rectangular books, desktops, cubicle partitions, computer monitors, ceiling tiles, HVAC vents, lights (below), and even the exterior windows and column grid (right) were shaped and arranged to accentuate cubes and rectangles.
The rectangular and square shape of our high-rise condo residential tower near downtown was attractive, yet similar to all others (right). We lived in a square and cubic world of man’s making. Our condo tower’s clean, cubic aesthetics looked modern inside and out. It was the unit’s kitchen, however, that first convinced us to buy (below). Although kitchen features were mostly white, our colorful dishes and other decor stood out. Clean lines and efficient layout of appliances, sink, and cupboards gave us ample room to work together.
The round overhead lights, round accent lights, curved faucet, and curved-back stools added enough non-cubic, accent ornamentation to the space, but not so much as would desecrate our home’s “cubic zone”.
As we stood in any room, we intuitively sensed the room’s directions for its use, based on our cubic, personal orientation within a room. Floor (gravity) was always down, and ceiling (sky) was always up. We defined forward as the direction toward a fireplace, a TV screen, a view window, or a bed headboard. We often faced the front of each room. Other directions – back, left, and right – were the default directions, dependent on our choice for the front. After defining our own cubic personal space within each room, we felt oriented, safe, and comfortable in each one.
Design With Squares and Cubes
Some say there are no 90-degree angles in nature. But gravity has provided up and down, and a small lake’s water is a practical, horizontal plane – at 90 degrees to gravity’s pull. Ignoring Earth’s curvature, and considering only a small plot of land, 90-degree angles are everywhere. In a house or a city, there is a built-in orthogonality everywhere.
Designers planning living spaces in our built environment – personal spaces, rooms, buildings, cities – most often use rectangles and cubes to lay out these spaces more simply and efficiently. This is because geometrically, squares and rectangles with 90-degree corners naturally tessellate on a floor plan to form room spaces. That is, these shapes can be placed side by side with no empty space between them (right).
Similar to squares tessellated on a 2D plane, cubic shapes with 90-degree corners tessellate in 3D space and are useful design tools for repetitious unit layouts. If these shapes are used in planning condo or hotel units, then identical modules using various cubic units can be stacked atop and adjacent to each other without gaps between them (below).
Structural elements in cubic buildings can efficiently be arranged – columns vertical and beams horizontal and orthogonal to each other –to fit cubic layouts. Walls and columns can more easily be aligned above and below to carry gravity loads down through a building.
Features within identical cubic unit modules – walls, ceilings, doors, kitchens, baths, and rooms can also be the same, leading to unitization of the whole building. Designing one module can design them all. Efficiency carries throughout – from unitized design to mass material procurement and construction organization.
Design and planning of city streets is usually square or rectangular in modern cities, but often is not in older cities. The map for a part of a city in Michigan was planned with orthogonal city streets and rectangular city blocks. Each block is regular in shape and similar to others. No one gets an odd-shaped building site, which are harder to survey and more complicated for building.
Streets are often numbered sequentially – 19th Street, 20th Street, 21st Street, and so on – to make street finding easier in the city. Streets run continuous in straight lines for miles without changing the street name.
Streets in old cities developed over the life of a city. Old cities, like Rome, were not originally surveyed and planned like new cities. Originally, paths leading radially towards town center became horse-drawn carriage roads, which over time became streets. Other paths ran circumferentially to connect radial paths. Now near an old city’s center, its street arrangement overlay old original pathways. The ensuing layout is often a tangle of radial, circumferential, and diagonal streets with odd-shaped city blocks.
Tourists to old cities see charm in their odd, random street layouts and non-cubic buildings. But I often get lost without an orthogonal layout. Ironically, the appeal of suburban plats in the last 50-75 years has been their curving streets and non-orthogonal layouts coupled with greenspace landscaping.
Dimensioning
Designing buildings and other structures requires dimensioned design elements on the contract drawings. Contractors need dimensions to fabricate, lay out, and construct elements on the ground and build up.
Cubic structures lend themselves readily to cartesian coordinates, our most common geometrical coordinate system for dimensioning buildings horizontally and vertically. Cartesian coordinates are named for Rene Descartes (1596-1650), who systematized orthogonal (cubic) grids into coordinate systems. Cartesian coordinates use 3 orthogonal axes: X, Y, Z and 6 directions along the axes: +X, -X, +Y, -Y, +Z, -Z from an origin at (0, 0, 0). The 6 directional vectors are each normal to a face of a cube, which makes it easy to dimension a cubic element.
If a project has more than one building or has skewed or curved elements, the design project’s geometry must be broken into sub-geometries so all points on a construction project can be dimensioned. Each separate sub-geometry with its own sub-origin (01, 01, 01) and its own axes, which are translated or rotated in space from the project origin (0, 0, 0).
Building Materials
Advent of the modern mass-produced, cubic construction unit was introduced by the Romans. Roman fired-clay bricks were used extensively to build new cities in the Empire far from Rome. Roman legions carried mobile brick kilns with them to assist in quickly constructing buildings. Clay was available near most new city sites; clay was packed into molds, then fired. Bricks, small single units, were lightweight, and were relatively easy to transport and lift with locally available carts and manual labor. Brickmaking and brick-laying technology, brought by Roman legions to new city construction sites in far-off regions of the Empire, was taught to local, manual laborers, many of the slaves.
Roman fired-clay bricks unknowingly helped introduce the concept of mass-produced cubic (rectangular) construction units to the world. At a brickmaking plant at a new project site, bricks were mass-produced by manual labor as regularly shaped, uniformly sized construction units. They could be provided readily and inexpensively at most Roman building sites. Bricks and mortar as construction units – in Roman and modern times – form geometric tessellations in construction walls, meaning they are tightly packed with no gaps between them. Bricks and mortar were placed into building walls quickly, without little sorting, trial fitting, cutting or notching.
Roman bricks were used in a variety of types of brick walls, depending on how bricks were arranged within the wall. The most common wall-building technique was Opus latericium, where bricks were placed as outer layers on each wall face. The wall’s core (center) was filled with Roman concrete (opus caementicium) (Figure ss).
Many modern construction units have flat surfaces that are available as cubic or square components – dimensioned lumber, plywood, concrete masonry units, doors, windows, concrete form panels, paving bricks, and welded wire fabric (see Figure xx below). Many construction elements are arranged in cubic or square configurations during construction – wood floor framing, reinforcing in shear walls, steel beams and columns, and slab reinforcing steel (see Figure xx below). Plywood, sheetrock, doors, and windows come in standardized sizes of two-dimensional units with standard thicknesses. Standardized flat items can be shipped anywhere in tight stacks, loaded and unloaded with forklifts. “Square” (right angled corners) and “flat” (stackable) are simple, basic properties of unitized, commoditized, construction materials everywhere. Flat, square units are easier to measure, cut, and construct, especially if a structure’s overall geometry is cubic.
Cubic or Square Building Materials (BELOW)
1 by F. Muhammad from Pixabay house-6076880_1920 2 by lucas-lenzi-hitgiH3QGMs-unsplash 3 by Pashminu Mansukhani from Pixabay forklift-835340_1920 4 by elvir-k-Xtyh5b5GGX4-unsplash 5 by saad-salim-PqRvLsjD_TU-unsplash 6 by tim-hufner-uryE1y31eTA-unsplash
MORE CUBES……….
Cubic Buildings 1 (BELOW)
First column (from top): concrete and masonry residence (Puerto Rico); hotel room (Kyoto); restaurant (Kyoto); “jelly-bean” row houses (St. John’s)
Second column (from top): high-rise residential tower (Toronto); hotel (St. John’s); new home (Peru); masonry towers (Alhambra)
Third column (from top): restaurant over water (Mexico); stone tower (St. John’s); residential tower (1)
(1) Photo by ena-begcevic-cO_O1YKWZbY-unsplash
Cubic Buildings 2 (BELOW)
First column (from top): modern residential units (Rotterdam) (1); Citadel Hill (Fort George) stone buildings (Halifax); wood building (Lunenburg); Government House (St. John’s)
Second column (from top): Elizabeth Tower – (Big Ben) (London); residence (Sanok); telephone booth (Kyoto)
Third column (from top): houses (Europe) (2); hedges at reflection pool (3); Amphitheater stonework (Caesarea); concrete construction (4)
(1) Photo by alicja-ziajowska-_vfSwqnSMwM-unsplash (2) Photo by francisco-moreno-ovgRb5WLWMQ-unsplash
(3) Photo by Peggychoucair from Pixabay hedge-4480080_1920
(4) Photo by tolu-olubode-PlBsJ5MybGc-unsplash
Other Cubic Things 1 (BELOW)
First column (from top): crop fields (Kauai); rail cars (Vancouver, BC); vehicle tires in steel racks (1); hat weaving pattern (Philippines); computer keyboard
Second column (from top): cartoon man carrying cubes (2); tissue box; home with large garden (Poland); concrete steps over rocks (St. John’s)
Third column (from top): wood joinery at shrine (Kyoto); notebooks in bookcase; railcar hallway with passenger compartments (Poland)
(1) Photo by Mediamodifier from Pixabay businessman-2108029_1920
(2) Photo by Pashminu Mansukhani from Pixabay forklift-835340_1920
Other Cubic Things 2 (BELOW)
First column (from top): inside passenger railcar (Osaka); monuments (Kyoto)
Second column (from top): decorated bus and delivery truck (Guatemala); carved box from Indonesia; colored pavers (San Diego)
Third column (from top): hallway on cruise ship; three-year-old granddaughter making a quilt.
NUMNUM Patterns 
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