Classical folding methods were subjects to be tested and studied in this semester’s design geometry classes. This has been very useful in introducing first year students with 3d euclidean constructions and using physical objects as reference to a digital model. Groups of students studied different folding methods and made both physical and digital models. Two of these methods were dominant in the class however, one of them was the variations of Miura-Ori, and the other one was Ron Resch’s famous folding pattern. Below are some models students made during their research. I’ll […]

## Courses » Architectural Geometry »

Again, seamless patterns are one of the main exercises of this semester’s architectural geometry class. It is expected to improve students reasoning on generative patterning while they explain their processes step by step. In between the random decision makings and the consciousness about the process, here are some of the student works: Sıla Yılmaz Seda Kasa Kaan Hiçyılmaz Göktuğ Balıkçı

While preparing the Geometry yearbook, I picked these four patterns from the 4th week assignment, “Seamless Patterns”. I still love to see how these patterns are generated by students with very limited knowledge on computer and geometry. There are other posts about this assignment here and here. Below are four from this semester; Ceren Atik Zeynep Dutipek Ceren Atik Meltem Bayrak

Unlike classical Pattern Deformation assignment discussed here and here, this time we asked students to explore deformations by using referential systems as a secondary space. They are expected to create variations on a regular pattern only by deforming its underpinning lattice. Below are three examples of this alternative assignment. I’m thinking about improving this exercise to three dimensions, seems very easy to implement by using cage editing commands of Rhino. Selin Işıldar Serra Uludağ Mine Güvenç

Below are some student works of this years Architectural Geometry / Pattern Deformations assignment. Students developed their own pattern deformation sequences mostly on regular hyperframes. Based on the classical Parquet Deformation exercise (discussed here), we tried to implement a rule-based approach in order to explore emergent patterns. The exercise seem to reveal endless improvisation potentials. Ece Erdoğdu İdil Side Erdoğan Bengisu Aydos Görkem Ünsal Mısra Sonat Göz Zehra Böhürler

In the third day of Architectural Geometry class, we’ve discussed about the regular tessellations, the famous triangle, hexagon and square tiles. Homework was to develop a custom referential system based on regular tessellations. We used popular explications of Islamic Patterns as inspirational examples, however we developed our own reference systems and patterns. Başak Konuşur Ceren Sezgin Ece Erdoğdu Görkem Ünsal Hüseyin Kuşçuoğlu Irmak Aşıkoğlu Zehra Böhürler Zeynep Dutipek

I learnt this method from the open math resources website. I couldn’t help myself repeat it in Rhinoceros. It was quite fun to solve circle tangency problems in 2D, this is one of them: drawing the circle that passes three given points, not using ready-made commands but only geometric tools of circle (compass) and ruler (line). Here is the sequence of it: First of all, we need to know that the circle we are looking for is centered at somewhere on the perpendicular paths between the points. This means, we […]

Here is a simple explanation about the famous Euclidean Constructions: Why didn’t Euclid just measure things with a ruler and calculate lengths? For example, one of the basic constructions is bisecting a line (dividing it into two equal parts). Why not just measure it with a ruler and divide by two? One theory is the the Greeks could not easily do arithmetic. They had only whole numbers, no zero, and no negative numbers. This meant they could not for example divide 5 by 2 and get 2.5, because 2.5 is […]

This is the examples of 2.5D exercises in design geometry course of freshman year of architecture. We asked students to create extruded or referenced solids referenced from their previous exercise of pattern deformations, (examples are here and here). We also started to inject some of the most used concepts of design computing here, by perceiving each tessellation cell as the variation of a predefined algorithm, such as a relationship with attractor object (a distance value with a point). This is therefore, more than a form finding experiment, slowly putting reference […]

In this exercise, students are asked to develop a method to produce custom tessellations. This is based on the analysis of what is called “islamic geometric patterns”. We have discussed about Erik Brough’s famous book, regarding geometric relationship and linear connectivities via underlying tessellations (such as regular square and hexagonal). Students, then created their own patterns along with their step-by-step explanations. Here are some results of it; Adnan Faysal Altunbozar Bahar Kaplan Cenk Toksöz Nilüfer Durmaz Nurseli Yorgancı Zeynep Albaş

First year Architectural Geometry course includes euclidean constructions as a study of associative geometry. We have exercised below questions to study this topic. These are three mutually tangent circles, that can be drawn using only compass and ruler, without built-in tangency functions in Rhino. Such exercises are expected to improve students’ reasoning. We believe architectural geometry education should encourage a conception that allows students to think about what they are doing and control their process, rather than just using commands to produce forms randomly.

Last week, first year architectural geometry course was about pattern deformations. Students are expected to familiarize with 2d drawing, transformation and control point editing commands while trying to design a deformation. After studying regular and semi-regular tessellations of the plane, they are expected to develop a reasoning on the rule-based and iterative processes. This also constructed an underpinning for Basic Design’s “Metamorphosis” study, where they have discussed about more conceptual frameworks derived from such systems. Below are some of the results from this one week exercise; Adnan Faysal Altunbozar Ayşe […]

Truncated Icosahedron (5,6,6) is an Archimedian Solid, probably the most popular one because of it’s apperance as the soccer ball. It’s constructed by trimming one third of each edge of an Icosahedron, (a Platonic Solid described here). In order to find 1/3’s of each edge, I used duplicate border, explode and divide commands to get the points that construct the pentagons and hexagons, while paneling is done by using planar surface commands on closed polyline edges. (If you are interested in how we reached the initial solid, refer to the […]

Tetrahedron is a popular platonic solid for designers. We’ve explained how to draw them using equilateral triangles here before. Recently I’ve found (sorry, lost the web adress) a much quicker way of modeling a Tetrahedron using a cube. It’s very simple, just connecting the three opposite corners of the cube automatically makes them equal, resulting the four equal faces. Of course this time you’ll have to calculate the actual edge length, but if you use “box diagonal” command, you’ll also have opportunity to set the edge length of the tetrahedron. […]

Octahedron is a platonic solid with 8 faces of identical equilateral triangles. It has a close relationship with cube as it’s dual. In order to construct an octahedron, we first have to create a square. Main problem of drawing the square is determining the right angle (perpendicular axis) to any point in euclidean space. We’ll draw it here as a two dimensional projection. However it can also be established in three dimensions with the same method (except using spheres instead of circles). Start from any two point in the space; […]

Dodecahedron is a Platonic Solid with 12 equilateral pentagonal faces. It has a close relationship with it’s 20-sided dual, Icosahedron. Mete Tüneri showed the following method of Dodecahedron construction, using only distances, corners of pentagon and a visionay equilateral triangle underneath. We’ll construct Dodecahedron, assuming that we’ve drawn an initial equilateral pentagon. We need to find out the pentagon’s angle of 3d rotation. First, put spheres at points a and c, with the radius of a to c. Intersection of these spheres result a circle. We know that, every point on […]

Icosidodecahedron is an Archimedian Solid, a thing in between the Platonic Solids of Icosahedron (d20) and Dodecahedron (d12). It is a rectified version of Icosahedron, constructed with dividing every edge of it into two equal segments, and joining these segments to create a composition of equilateral pentagons and triangles. Archimedian Solids consists of at least two equilateral polygons, whereas Platonic Solids are constructed by only one. We’ll deduce an Icosidodecahedron from Icosahedron below; First, you should create an Icosahedron, the Platonic father of Icosidodecaheron. After that, all faces should be […]

Icosahedron is one of the five Platonic Solids with twenty equilateral triangular faces. It’s dual is Dodecahedron, which has pentagonal faces. Here, Icosahedron is constructed by using pentagons. Interesting thing is it’s close relationship with Dodecahedron, although they seem to be very different. This time we won’t lose time with two dimensional pentagon drawing. Maybe we’ll discuss that later. Assuming you’ve created a regular pentagon, you should find the “tip” point of the Icosahedron by intersecting spheres from at least three of the corner points with a radius of pentagon’s […]

Truncated Tetrahedron is an Archimedian Solid, created by slicing a Tetrahedron. It’s faces are regular hexagons and triangles. Assuming you’ve created a Tetrahedron, first join it’s faces to create a polysurface. Now, you may re-create the lines of Tetrahedron’s edges, either by drawing them or generating them (Curve/Curve from Objects/Duplicate Edge). While the edge lines are selected, hit (Curve/Point Object/Divide Curve By/Number of Segments) and type 3 to the number of segments to be created. Now all edges should be divided equally into three parts. Draw the equilateral triangles, connecting the […]

Tetrahedron is a platonic solid with 4 equal triangular faces (which are also equilateral), 6 equal edges and 4 vertices. While creating this shape, we will take a closer look at length transfers using compass-like tools both in two and three dimensional space. In order to define the edge length of first triangle (which is a straight line), start with any two points in cartesian space. Using compass (arc or circle), draw two arches (or circles) using your initial points as corners, and the distance between your points as radius. […]