We will prove that if a one-to-one mapping <mml:math alttext="$f:\mathbb{R}^3\rightarrow\mathbb{R}^3$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi><mml:mo>:</mml:mo><mml:msup><mml:mi>&#8477;</mml:mi><mml:mn>3</mml:mn></mml:msup><mml:mo>&#8594;</mml:mo><mml:msup><mml:mi>&#8477;</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:math> preserves regular hexahedrons, then <mml:math alttext="$f$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi></mml:math> is a linear isometry up to translation.

International Journal of Mathematics and Mathematical Sciences

Mappings preserving regular hexahedrons

Abstract

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