Let H be an induced subgraph of the torus $C_k^m$. We show that when $k\ge 3$ is even and $|V(H)|$ divides some power of k, then for sufficiently large n the torus $C_k^n$ has a perfect vertex-packing with induced copies of H. On the other hand, disproving a conjecture of Gruslys, we show that when k is odd and not a prime power, then there exists H such that $|V(H)|$ divides some power of k, but there is no n such that $C_k^n$ has a perfect vertex-packing with copies of H. We also disprove a conjecture of Gruslys, Leader and Tan by exhibiting a subgraph H of the k-dimensional hypercube $Q_k$, such that there is no n for which $Q_n$ has a perfect edge-packing with copies of H.

令H为圆环的诱导子图$C_{ķ}^{米}$。我们表明$ķ\ge 3$ 甚至 $|V（H）|$除以k的一些幂，然后对于足够大的n个圆环$C_{ķ}^{ñ}$具有诱导H的完美顶点堆积。另一方面，证明格鲁斯利的一个猜想，我们证明当k为奇数而不是素数时，则存在H使得$|V（H）|$除以k的一些幂，但没有n使得$C_{ķ}^{ñ}$具有H的完美顶点堆积。我们还通过展示k维超立方体的子图H来反驳Gruslys，Leader和Tan的猜想${问}_{ķ}$，使得没有Ñ为其${问}_{ñ}$具有与H的副本的完美边缘堆积。