Abstract A tensegrity family is a group of tensegrity structures that share a common connectivity pattern. The three first members of the Octahedron family are the octahedron, the expanded octahedron and the double-expanded octahedron. In this work a new family is presented: the X-Octahedron family. If in the elementary rhombic cells of the Octahedron family a diagonal cable is introduced then X-rhombic cells are obtained, resulting in tensegrity forms that belongs to the new family. Three members of the family have been obtained: the X-octahedron, the X-expanded octahedron and the X-double-expanded octahedron. Several element groupings have been considered in order to find new equilibrium shapes of the members of the new family. The values of the force:length ratios which satisfy the super-stability conditions have been computed analytically.

中文翻译：

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八面体族作为张拉整体族的来源：X-八面体族

摘要 张拉整体族是一组具有共同连接模式的张拉整体结构。八面体家族的前三个成员是八面体、扩展八面体和双扩展八面体。在这项工作中，提出了一个新的家族：X 八面体家族。如果在八面体族的基本菱形单元中引入斜线，则获得 X 菱形单元，从而产生属于新族的张拉整体形式。已获得该家族的三个成员：X-八面体、X-展开八面体和X-双展开八面体。为了找到新族成员的新平衡形状，已经考虑了几种元素分组。满足超稳定条件的力：长度比值已被解析计算。