Symmetries

This Painted Trillium, which I photographed a few years ago in the Catskill Mountains, has D3 symmetry type. Lots of flowers have rotational symmetries … what other mandalas occurring in nature do you like? Any natural border patterns?

I was looking online and I found this Versace scarf that has rotational mandala symmetry!

The Yin and the Yang united, seeing through the eyes of the One.

Photo captured in my living room

Demetrios Benetos

I saw these beautiful mandalas and border patterns during my visit to Dublin Castle a few years ago.

Michael Blaine

Objects with rotational symmetries, which we’ll call “mandalas”, occur in many cultures. The mandala gallery will show some examples.
To celebrate St. Patrick’s Day, here are two Celtic crosses. The first is from the Gallarus Oratory in Ireland, and has symmetry type D4. The second one, which is a Z4, is from Santiago de Compostela in Spain.

An internet image search for mandalas will reveal many and varied images characterized by rotational symmetries. How do their classifications compare with the Himalayan mandalas in the Rubin Museum?

Currently on display at the Rubin Museum of Art are eight mandalas. As you ascend the 2nd to 4th floors, you meet:

Mandala of Guhyasamaja
Mandala of Chandra
Mandala of Amoghapasha
Naga Mandala Assembly
Guhyasamaja Manjuvajra Mandala
Medicine Buddha Mandala
Lotus Mandala of Hevajra (3-dimensional)
Mandala of Peaceful and Wrathful Deities of the Bardo

Mandala of Chandra

Let’s analyse these in terms of their rotational mandala classifiers. For example, the Lotus Mandala and the Mandala of Chandra are built around the submandala <8>, while the others use <4>. What other common submandalas and features do they have? What are the differences between them?

This blog will explore symmetry types as manifested in mandalas, in the streets of Manhattan, and beyond. It is for students in Professor Kirby’s classes, and anyone else who’s interested in spinning out the mathematical ramifications of mandalas and border patterns.