Symmetry in Thirty-two Planes

Muqarnas Domes in a Symmetry Family

In prior work I investigated numerous novel methods for developing muqarnas* / mogharnas** compositions. These included a wide variety of domes, onion domes, flattened domes, hybrid flattened domes, seeded compositions, composite forms, spiral staircase ceilings, enclosing forms, and unique forms. (*Muqarnas, Arabic transliteration. **Mogharnas, Persian transliteration.)

What follows is a brief exploration of using symmetry as a means of developing novel mogharnas / muqarnas domes. Some are domes, some are onion domes, but all are sequential members of a series of muqarnas / mogharnas domes related by symmetry. Each member of the series is represented by a YouTube video and a plan view diagram. The diagram indicates the planes of symmetry and how the first and second tier of the dome is derived from the central traditional dome.

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Because the simplest example of the series is not particularly pleasing I chose to present the most complex first. There are five members of the series with 32, 16, 8, 4, and 2 planes of symmetry each. all planes are vertical and all intersect at equal angles at the center of the plan view of the dome. At the end I have included an additional example of 2 planes of symmetry which is more complex.

All the diagrams represent the central dome on top of the prior YouTube animation. The two colors indicate the way the central dome is expanded on the successive tiers. The final example of necessity uses six colors as a guide to its expansion.

Symmetry in Thirty-two Planes

Symmetry in Sixteen Planes

For anyone designing mogharnas / muqarnas special care must be taken when determining the symmetry determined by the muqarnas / mogharnas tiles themselves. I happened to choose 32 tiles to complete the circle. I could as easily have chosen 36, 30, 27 or any other number. Thirty-two being a power of two possesses properties which may have made it a felicitous choice on my part.

Although I said the 32 planes of symmetry example is the most complex, in a very real sense the opposite is true. Two adjacent ‘pie’ slices multiplied thirty-two times creates that dome. Each slice is made of only 1/32 of the total mogharnas / muqarnas tiles. On the other hand the examples with two planes of symmetry are made of two pieces with half of the dome in each piece. So in a counter-intuitive manner the most complex symmetry is much easier to construct than the simpler symmetry.

Symmetry in Eight Planes

Symmetry in Eight Planes

Although even I find it difficult to describe the rule that I use to increase the symmetry complexity, I hope it is evident in the diagrams themselves.

For those of you who are still here, this is my gift of sorts to you. Sharing the same symmetry group as the example immediately above, but very different in appearance is the following dome. Instead of just two elements (blue and green), it has four additional elements. This gives rise to a completely different appearance than its two planes of symmetry counterpart immediately above.

Symmetry in Eight Planes

Symmetry in Eight Planes

For those of you brave souls who made it to the end. Thank you for your strength of character, endurance and persistence. You’re the best!

Dan Owen, originally posted on LinkedIn, September 13, 2016