There is also something unpleasant to the eye in the sharp angles which form the three _arêtes_ of the tetrahedron; it looks as if there had been a lack of material, and as if the structure would suffer in consequence. The four-sided pyramid has more dignity and more amplitude; its four faces, placed back to back in pairs, seem to counterpoise and sustain each other in a fashion which is impossible in the case of the tetrahedron. [Illustration: FIG. 128.--Plan of the Pyramid of Cheops.] The one characteristic possessed in common by those relics of the Ancient Empire which we call pyramids, is their four-sidedness. To an attentive observer these buildings offer more diversities than would at first sight be believed. From Meidoum in the south to Abou-Roash in the north is a distance of 43-1/2 miles as the crow flies. Between these two points, which may be called the northern and southern boundaries of the pyramid field, about one hundred have been discovered, sixty-seven of which have been examined by Lepsius. Now, in this whole number there are not two which resemble each other in all particulars, or which seem to be copies of one model. We do not refer only to their height, which differs in an extreme degree. The three large pyramids at Gizeh are 482, 454, and 218 feet high respectively, while at their feet are several little pyramids which hardly exceed from 50 to 70 feet of vertical height. Between these two extremes many of intermediate sizes may be inserted. The Stepped Pyramid, near Sakkarah, is about 190 feet high; the largest of those at Abousir is about 165; one of those at Dashour is not quite 100 feet. These differences in height are easily explained by one of those national habits to which we have already alluded. Every Egyptian, as soon as he arrived at years of discretion, set about building his own tomb. He dug the well and the mummy chamber, he caused the sarcophagus to be carved and the funerary chapel to be built. It often happened that those who had ordered such works died long before they were finished, and it would seem that their heirs were content with doing no more than was strictly necessary. They placed the mummy in its grave with the prescribed ceremonies, they filled up the well and sealed the private parts of the tomb; but being occupied with the preparations for their own funeral, they did not continue the decoration of the chapel, which thenceforward remained _in statu quo_. Thus only can we explain the state in which several important tombs have been discovered both at Memphis and at Thebes. On one wall we find paintings and sculptures carried out with the greatest care and finish, while on another nothing is to be seen but the first rough outline, in red paint, by the artist charged with the undertaking. The completion of the work must have been suddenly arrested by the death of the destined inhabitant of the tomb. [Illustration: FIG. 129.--The great pyramid and the small pyramids at its foot; from Perring.]