Motivated by recent progress in research on extending holomorphic functions defined on subvarieties of classical domains and their connections to 3-point Pick interpolation, we study a special class of two-dimensional algebraic subvarieties, denoted as $M_{\alpha }$, within the unit tridisc. These subvarieties are defined as sets of the form$\{(z_1,z_2,z_3)\in {\mathbb{D}}^3:{\alpha }_1{z}_1+{\alpha }_2{z}_2+{\alpha }_3{z}_3={\bar{\alpha }}_1{z}_2{z}_3+{\bar{\alpha }}_2{z}_1{z}_3+{\bar{\alpha }}_3{z}_1{z}_2\}.$ In this paper, we demonstrate that for a given non-degenerate extremal maximal 3-point Pick problem, there exists an α such that $M_{\alpha }$ appears as its uniqueness variety. Additionally, we describe several geometric properties of $M_{\alpha }$ and show the biholomorphic equivalence between any two surfaces $M_{\alpha }$ and $M_{\beta }$, where the triples α and β satisfy the so called triangle inequality.

受最近在扩展经典域子类上定义的全纯函数及其与 3 点 Pick 插值的联系方面的研究进展的推动，我们研究了一类特殊的二维代数子类，表示为${\mathrm{中号}}_{\alpha }$，在单位三圆盘内。这些子品种被定义为以下形式的集合$\{（z_1,z_2,z_3）\epsilon {\mathbb{D}}^3：{\alpha }_1{z}_1+{\alpha }_2{z}_2+{\alpha }_3{z}_3={\bar{\alpha }}_1{z}_2{z}_3+{\bar{\alpha }}_2{z}_1{z}_3+{\bar{\alpha }}_3{z}_1{z}_2\}。$在本文中，我们证明对于给定的非退化极值最大 3 点选择问题，存在一个α使得${\mathrm{中号}}_{\alpha }$以其独特的品种而出现。此外，我们还描述了${\mathrm{中号}}_{\alpha }$并显示任意两个曲面之间的双全纯等价${\mathrm{中号}}_{\alpha }$和${\mathrm{中号}}_{\beta }$，其中三元组α和β满足所谓的三角不等式。