抄録
The rotation and rotary inversion of textile weaves are classified into 8 groups as shown in Table 1. and it is shown that theses uccessive operation makes an Abelian group as Table 2.
The conditions to be complete even-sided weave are: (1) the weave has reversion symmetry in respect to warp or/and weft way, and (2) the wecve has screw symmetry in respect to warp or/and weft way.
There are 27 types of symmetry satisfying these conditions. The examples of the weaves are shown in Fig.4 using 8 harness weaves.
The weaves (1) to (5) in Fig.4 and Table 3 have reversion symmetric axes along warp and weft. These are independent of the operations CY and CX, known as “the complete even-sided weave of the stkind”. The weaves (6) to (18) have reversion symmetric axes along warp or weft. These weaves transform to the equivalent weaves of the 2nd kind, by the operation CY. This is type of “the comglete even-sided weave of the 2nd kind”. The weaves satisfying the condition (2) belong to (19)-(27). These transform to the half-slided weaves along the warp-way of initial weaves, by the operation CY, knowd as “the complete even-sided weave of 3rd kind”.
