This house by Chilean firm Moure Rivera Arquitectos is based on Euclidean mathematics, the earliest known system of geometry.

Located by the beach in Santo Domingo, Dominican Republic, the house has a steel frame and is clad in fibre cement.

In incorporates a barbecue and terrace area on the roof.

Here's some more information from Moure Rivera Arquitectos:

The house A comes from a reflection and study the structures generated by implicit form, where part by depriving the subject of its traditional meaning or associations, where it discharge or reduction of meaning emerged only by functional approaches. By changing the visual design and the perception of these forms, considering the object from formal positions over space and time, as a sign or fragments detached from a conventional meaning, they acquire meaning in themselves.

This is to prove that they can not depart from the intent, if not to the contrary is possible the knowledge of architecture starting from the object. The world of the object is capable of making these purposes without being those imposed by the form.

In the process poses a 13.68 square meters of hand, this measure went through the study of possibilities in the field in which the house would be projected. The square and recognizing elements, ratios and proportions is created the first intention. The first stage is abstract and is information from which you can find many solutions for different purposes such three-dimensional structure.

It shows the use of tools to generate the form, specifically Euclidean geometry, in the example of the house to give each of these steps prior to design, which makes recognition of the relations and elements that generate the form. These diagrams include not only analytical pre-design stages, but also part of it, since it is a symbiotic process.

The square or regular hexahedron, is a dialectic between two-dimensional problem and three-dimensional space when viewed through the architectural representation. We see the representation through the object and not the object through the observer. No occupying the conical perspective, given through sketches or 3D representations showing what the observer sees and not what the object is.

For the study of object occupy the method used at the beginning of the modern movement where we quote Theo Van Doesburg, and Alberto Sartoris, especially after studying charts of Peter Eisenman. It's about creating an architectural object can be generated by itself. With purpose, language and self-representation.  The plane of the square as the first two-dimensional and three-dimensional axionometric are the generators of diagrams and sequences of order to the creation of the new architectural for.

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From this sequence and an order given by the harmonic division of the square of 187 m2. and through this subdivision are shaped the guidelines of the three-dimensional shape. It starts with the diagonal of the square which is lowered to generate a greater projection of the original item, taking these two elements and begin to divide through the intersection of the arc and the diagonal of these elements.

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This is done is to generate the possible plot or grid in which the first structures were generated in the house.

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In the first intersections of the diagonal and the arc of the square began to plot the lines parallel to the sides of the element. With this new auxiliary lines generated new squares and rectangles of different sizes to which they rebuilt their own arcs that intersect diagonally again producing new points of intersection which will produce new horizontal and vertical lines.

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This process is repeated systematically until a generous amount of auxiliary lines to put together our new fabric or grid. The same is obtained in three dimensions.

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Parallel program is measured in rectangular sizes generated by square footage.Then he organized through the relationships that could be inside the square.

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Having these two elements and configured, plot and program overlap to generate the plot lines to found the first horizontal and vertical structures of the house.

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The lines given by juxtaposition, are extruded to form the axionometric along the lines of the house. Then through a series of surgical removal of this body mass generated by the juxtaposition quadrants where they were not occupying. The lines are always in relation to refine the chosen fabric and creating the new empty mass of the house.

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The house has a program developed in 187 m2, inside has 4 rooms, three bathrooms, a living room, kitchen, loggia, barbecue area and terraces.

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