This work investigates flexible Kokotsakis polyhedra with a quadrangular base of equimodular elliptic type, filling a significant gap in the literature by providing the first explicit constructions of this type together with an explicit algebraic characterization in terms of flat and dihedral angles. A straightforwardly constructible class of polyhedra - called quasi-symmetric nets (QS-nets) - is introduced, characterized by a symmetry relation among flat angles. It is shown that every elliptic QS-net has equimodular elliptic type and is flexible in real three-dimensional Euclidean space (rather than only in complex configuration spaces), except for a few exceptional choices of dihedral angles, and that its flexion admits a closed-form parameterization. Examples are constructed that are non-self-intersecting and belong exclusively to the equimodular elliptic type. To support applications in computational geometry, a numerical pipeline is developed that searches for candidate solutions, verifies them using the explicit algebraic characterization, and constructs and visualizes the resulting polyhedra; numerical validations achieve high precision. Taken together, these results provide constructive criteria, algorithms, and validated examples for the equimodular elliptic type, enabling the design of a broad range of flexible Kokotsakis mechanisms.

翻译：本研究探讨了具有等模椭圆型四边形底面的柔性Kokotsakis多面体，通过首次提供该类型的显式构造及其基于平面角和二面角的显式代数表征，填补了文献中的重要空白。文中引入了一类可直接构造的多面体——称为拟对称网（QS-nets）——其特性由平面角间的对称关系所表征。研究表明，除少数特殊的二面角选择外，每个椭圆型QS-net均具有等模椭圆型，并在实三维欧几里得空间（而非仅复构型空间）中具有柔性，其屈曲运动允许闭式参数化描述。研究构造了非自相交且完全属于等模椭圆型的具体实例。为支持计算几何应用，开发了一套数值流程：搜索候选解，利用显式代数表征进行验证，并构建和可视化所得多面体；数值验证达到了高精度。综合而言，这些成果为等模椭圆型提供了构造性判据、算法及验证实例，为设计各类柔性Kokotsakis机构奠定了基础。