The xoloitzcuintle is one of several hairless Mexican dog breeds. They come in various sizes from standard to miniature, and some can indeed grow coats of fur. The hairless variant is also called the Mexican hairless dog. The name is Nahuatl in origin and is derived from the god Xolotl plus the Nahuatl word for dog, itzcuīntli.

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Xoloitzcuintle (Wikipedia)