"A three-dimensional object in which there is no distinction between inside and outside." An extended version of the Möbius strip → The surface is connected → If we create it in our 3D space, we will inevitably break through it midway. When it becomes an architectural space As I was walking down the corridor Without realizing it It's on the back side of the building Neither the walls nor the floor are cut. A single continuous surface "Architecture where the interior and exter

Some complex functions are "contradictory in the ordinary plane." Instead of using a single flat surface, stack multiple flat surfaces on top of each other. Then, in the first order, √z = + and in the second order, √z = − can exist without contradiction. "Architecture where different levels of space exist within the same location." For example, a space where you enter the same door but end up on a different floor—like a "door to anywhere." "Create space to match the function"

A structure where space is made up of bundles of circles (fibers) → Link (chain link) state "One of the most beautiful geometric structures in the universe" ホップ・パビリオン "Imagination condition" category Set conditions Environment settings A city waterfront. The reflection of structures on the water's surface suggests the symmetry of $S^3$. lighting Twilight (blue hour). The setting is such that the afterglow from within highlights the overlapping curves. texture Parametric ribs

One of the most complex symmetries conceivable in the universe. Mathematics dealing with the symmetry of continuous transformations 248 fundamental symmetry directions → 8-dimensional symmetrical lattice → jewel-like structure Cosmic Gothic Structure Music, Art, Mathematics, Light, Silence 静かなコンクリートの宇宙 宇宙の星座

There is order, but no cycle. The golden ratio appears. A star-shaped pattern is created. No matter how much you expand it, it won't be the same cycle. Self-replicating urban structure → Order + Non-repetition Quasicrystal 迷う文化ホール

Strange Structure of Higher-Dimensional Spheres It's the same ball, but it's a different ball. An exotic sphere is a smooth manifold that has the same homotopy type (topological structure) as a normal sphere, but possesses a different smooth structure (differential structure). 一番理解しにくい構造 4次元球面のエキゾチック構造