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Symmetry 2018, 10(7), 275; https://doi.org/10.3390/sym10070275

Reflexively-Fused Cylinders

Meiji Institute for Advanced Study of Mathematical Sciences, Tokyo 164-8525, Japan
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Received: 8 June 2018 / Revised: 28 June 2018 / Accepted: 29 June 2018 / Published: 12 July 2018
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Abstract

The present paper introduces a method for designing 3D objects that are initially incomplete, but become complete when they are augmented by their mirror reflections. Physically, the mirror image is plane-symmetric with respect to the original object, but the perceived shape is not necessarily symmetric because of optical illusion. In the proposed method, a 2D shape that is not necessarily symmetric is divided into two halves, one of which is used to construct a solid object. When we place the solid object on a plane mirror, the other half is generated by the mirror, and thus, a whole shape is realized. In the present study, the design algorithm and examples are shown, and the condition for constructability is also presented. View Full-Text
Keywords: mirror; optical illusion; ambiguous cylinder; impossible object; anomalous symmetry mirror; optical illusion; ambiguous cylinder; impossible object; anomalous symmetry
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Sugihara, K.; Moriguchi, M. Reflexively-Fused Cylinders. Symmetry 2018, 10, 275.

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