Contemporary with the Alhambra, the Real Alcázar of Seville, Spain was rebuilt in 1364 as a palace for Dom Pedro, Christian king of Castile (1334 - 1369) in the Mudejar style. (Muslims who chose to live under Christian rule were known as mudéjares). Although there have been alterations and additions over the centuries, this remarkably well-preserved palace was originally built by a Christian ruler in the Islamic style of Andalusia and retains its Islamic character, containing some of the most beautiful examples of Mudejar alicatado (Spanish, for cut tiles, derived from the Arab verb qataa, to cut) from this time period. Since all 17 planar crystallographic groups are now believed to be represented in the tilings of the Alhambra, one wonders if the same may be said of the ornament found in the Alcázar. This paper will briefly discuss the history of the Alcázar, illustrate and classify some of the planar designs as to the isometries they permit and then attempt to answer the salient question broached in the title of this paper.