| Summary: | The main aim of the paper is to give the crossing number of the join product <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>G</mi><mo>*</mo></msup><mo>+</mo><msub><mi>D</mi><mi>n</mi></msub></mrow></semantics></math></inline-formula>. The connected graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>G</mi><mo>*</mo></msup></semantics></math></inline-formula> of order six is isomorphic to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>K</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>\</mo><mi>e</mi></mrow></semantics></math></inline-formula> obtained by removing one edge from the complete bipartite graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>K</mi><mrow><mn>3</mn><mo>,</mo><mn>3</mn></mrow></msub></semantics></math></inline-formula>, and the discrete graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mi>n</mi></msub></semantics></math></inline-formula> consists of <i>n</i> isolated vertices. The proofs were carried out with the help of several possible redrawings of the graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>G</mi><mo>*</mo></msup></semantics></math></inline-formula> with respect to its many symmetries.
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