How to 3d-Model a Byzantine-Styled Octagonal Dome

I work as seminar lecturer and literary translator. I am a published author, and graduate of the University of Essex (BA in Philosophy).

The Byzantine dome

The dome is found in virtually all Byzantine religious architecture, and often in large numbers in the same monument. A central, imposing dome, will be surrounded by smaller ones, and even the side structures may be covered with miniature versions of this formation.

In this brief tutorial we will examine how to model a simple dome, in the Byzantine style, using primitives in a 3d-modeling program. The screens are from Blender, but the method is the same in all software that uses editing of vertices.

First step in modeling an octagonal dome

In this step you create the base where the dome is to rest. We start with a cylinder. If your software allows you to set the number of sides the cylinder has (in Blender, for example, this option is easily accessible from the "properties" menu) you simply set that number to 8; Figure A shows the result.

Otherwise, you will have to manually construct a perfectly octagonal volume. There are a number of ways to do so. Those may be covered in depth another article, but for the time being it can be noted that a perfect octagon is inscribed in a sphere, and this happens when the length of each side of the octagon is roughly 2,43 times larger than its width. In Figure B you can see this ratio, in a parallelogram inscribed to the analogous circle.

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Second step in modeling an octagonal dome

Now you have to create the lower, flat cover of the dome. This is more economically done by using the base which has already been created, and editing its top part. So, we start by editing the top surface of our cylinder: we are to work with vertices, and have to link any two of them, so as to subdivide and acquire a new point in their middle. This is shown in Figure C.

Now we extrude this point, to a small height (the height should be small, because the basic cover of the dome is typically low). Afterwards we simply create surfaces by linking all the eight original vertices with the central point we created. The process is presented in Figure D. You can also erase the edges you created in the first part of this step (the linked original vertices), prior to moving to the final part of the step, or afterwards. In Figure D those edges have been removed.

Third step in modeling an octagonal dome

All that remains is to add the top part of the dome. For this a sphere is to be used. In general, the top of a Byzantine dome is virtually a sphere which has roughly 9/10 of the periphery of the sphere the dome’s base was inscribed on. So you just place the generic sphere your program uses (in Blender it would already be positioned in accordance to your base), and alter its volume correspondingly. The result is shown in Figure E.

Other possible steps

You can always add more elements to a dome. In this article we only presented the basic forms needed. In a future article we will have a look at how to easily create windows or decorative openings for the walls supporting the dome, or how to include arches and other elements for the top.

Another article on modeling Byzantine architectural forms

• What Is a Pendentive Form and How to 3d-Model It
An article on how to create a 3d model of the architectural feature known as the pendentive; a sphere cut in triangular slices. The pendentive is a major characteristic of Byzantine – and later – architecture. In this tutorial I used Blender, but it