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Parameter-free theoretical predictions based on a dual shell mechanism within the proxy-SU(3) symmetry of atomic nuclei, as well as covariant density functional theory calculations using the DDME2 functional indicate that shape coexistence (SC) based on the particle-hole excitation mechanism cannot occur everywhere on the nuclear chart but is restricted on islands lying within regions of 7–8, 17–20, 34–40, 59–70, 96–112, 146–168 protons or neutrons. Systematics of data for even-even nuclei possessing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> (beta) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula> (gamma) bands support the existence of these islands, on which shape coexistence appears whenever the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> bandhead <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mn>0</mn><mn>2</mn><mo>+</mo></msubsup></semantics></math></inline-formula> and the first excited state of the ground state band <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mn>2</mn><mn>1</mn><mo>+</mo></msubsup></semantics></math></inline-formula> lie close in energy, with nuclei characterized by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mn>0</mn><mn>2</mn><mo>+</mo></msubsup></semantics></math></inline-formula> lying below the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mn>2</mn><mn>1</mn><mo>+</mo></msubsup></semantics></math></inline-formula> found in the center of these islands. In addition, a simple theoretical mechanism leading to multiple-shape coexistence is briefly discussed.