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Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula> be a family of sets in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup></semantics></math></inline-formula> (always <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>). A set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>⊂</mo><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup></mrow></semantics></math></inline-formula> is called <i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-convex</i>, if for any pair of distinct points <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><mi>M</mi></mrow></semantics></math></inline-formula>, there is a set <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>∈</mo><mi mathvariant="script">F</mi></mrow></semantics></math></inline-formula>, such that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi><mo>,</mo><mi>y</mi><mo>∈</mo><mi>F</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>⊂</mo><mi>M</mi></mrow></semantics></math></inline-formula>. A set of four points <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>{</mo><mi>w</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>}</mo></mrow><mo>⊂</mo><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup></mrow></semantics></math></inline-formula> is called a <i>rectangular quadruple</i>, if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>conv</mi><mo>{</mo><mi>w</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>}</mo></mrow></semantics></math></inline-formula> is a non-degenerate rectangle. If <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula> is the family of all rectangular quadruples, then we obtain the <i>right quadruple convexity</i>, abbreviated as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mi>q</mi></mrow></semantics></math></inline-formula>-<i>convexity</i>. In this paper we focus on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mi>q</mi></mrow></semantics></math></inline-formula>-convexity of complements, taken in most cases in balls or parallelepipeds.