The purpose of this article is to propose a new design for the periodic table of elements. The new design is based on a three-dimensional (3D) model of the gastropod shell structure and presents a mechanism of the formation of elements that reflects the laws of nature that guide the formation of the gastropod shell, electron orbitals, and element structure. The author also identifies challenges associated with the current standard periodic table, such as the positions of hydrogen, helium, lanthanides, and actinides. The author’s research is a response to the IUPAC’s request, dating back to 2016, to settle unresolved disputes surrounding the current standard periodic table. Hence, the author proposes the “Gastropod Shell Model”, which presents the periodic system in 2D and 3D snail shells based on a hypothesized unifying principle guiding the formation of elements: the universal unified theory that considers the spiral and vortex forms as the bridge between energy and matter. The author was able to position hydrogen, helium, lanthanides, and actinides uniquely in their proposed periodic system to solve problems associated with their positions in the standard periodic table. Readers will be interested in uncovering the “hypothesized unifying principle guiding the formation of elements”.