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Group Show of Contemporary Artists 2021, 
”A4 Self-restraint / Self-body”
Tokyo Metropolitan Art Museum Gallery A


This art work is three-dimensional art that uses only two types of parts. It is composed of two rhombic hexahedrons (acute, obtuse) with the golden ratio. The assembled model perfectly represents the quasicrystal* structure, the three-dimensional Penrose model.
* “Quasicrystal” is described in Additional INFORMATION
Self-similarity can be partially observed in this structure. However, since the period of this structure is an irrational number, there is no repetition pattern. In other words, it is not possible to make a copyable unit cell. In order to express the contrast with this art work structure, at the exhibition at the Tokyo Metropolitan Art Museum, I used a rectangular frame with self-similar shapes and repeating patterns as a pillar.

この作品は、2種類の部品だけを使った立体作品である。黄金比を内包する二つの菱型六面体(鋭形菱型六面体acute、扁平菱型六面体obtuse)で構成される。組み立てられた造形物は、準結晶構造、三次元ペンローズモデルを完璧に表現している。(準結晶はAdditional INFORMATIONで記述)


The structure of this art work is based on the structure of a substance called “quasicrystal”. I majored in solid state physics at graduate school and was doing research on “quasicrystals”. The idea of this art work goes back to here 30 years ago.
Self-similarity is partially observed in “quasicrystals”. However, since the period of the crystal lattice is an irrational number, there is no repeating pattern. This structure grows disciplinedly, and even when it reaches the moon, this structure cannot meet its own alter ego.
I think that the task of assembling the parts of this art work is to meet one’s alter ego beyond infinity. It resembles an endless journey facing discipline and indiscipline, stability and instability, continuity and discontinuity, liberty and control.
I chose this structure to represent the middle of the journey.


Additional INFORMATION 1/2 : Brief description of “quasicrystals”

Quasicrystals changed the definition of crystals in 1991. This crystal actually exists. Shechtman et al. announced the results of the study as a “quasicrystal” in 1984 and received the Nobel Prize in Chemistry in 2011. The period of the crystal lattice is an irrational number. In other words, We can imagine a crystal with an infinite size unit cell. It has a structure described by three-dimensional Penrose tiling, and has mathematical phenomena such as golden ratio, five-fold symmetry, Fibonacci sequence, and self-similarity. Since before 1984, it is well known that these mathematical phenomena are found in nature such as plants, organisms, and viruses.


Additional INFORMATION 2/2 : 昔の話 My story 

from Excerpt from the flyer of the exhibition ”A4 Self-restraint / Self-body” @ Tokyo MAM


当時、支援してくださった、安川寿之輔先生に感謝を込めて ここに記します。