( 70 ) 



ce, S[h) — aO, 30, 30, 10) - (50, — — , 5^). 



This figure oan be deduced from fig. 3 by moving the limiting 

 bodies of vertex import, i.e. the dT projected as trapezoids (12, 13, 

 14, 15), (23, 24, 25, 21), etc. in such a way towards the centre, 

 that the ten original edges of >S(5), i. e. the five edges (12, 21), 

 (23, 32) etc. and the five edges (52, 25), (13, 31), etc. disappear. 

 It is easily shown that these two conditions do not collide; for, if 

 we suppose that the trapezoid (12, 13, 14, 15) remains where it is, 

 whilst of the two adjacent trapezoids (21, 23, 24, 25), (51, 52, 53, 54) 

 the first experiences a rectilinear translation 21, 12, the second a 

 rectilinear translation 51, 15, the vertices 52 and 25 will coincide 

 in the point of intersection of the projections (12, 14), (13 15). So 

 we get the simple result of fig. 17, where the limiting polygon is a 

 pentagon with side (/, oppositely orientated with respect to fig. 1". 

 In fig. 17 the six points where the digit 1 is lacking form the vertices 

 of an of body import, the four points where the digit 1 occurs 

 a T of vertex import, etc. 



ce,e. Sip) — (30, 60, 40, 10) — {htT, — , -, 5^7'). 



This figure can be derived from fig. 11 by moving the 5/7' of 

 vertex import towards the centre in such a way that the ten prisms 

 1\ of edge import disappear. Then the triplets of parallel edges of 

 these 7*3 disappear and only the two coinciding endplanes remain. 

 But this implies that the five tO of body import are reduced to tT 

 by the annihilation of these edges; so in the case of fig. 12 the 

 square (532, 352, 354, 534) is reduced by the coincidence of the 

 vertices 532, 352 and of the vertices 354, 534 to an edge with the 

 direction (532, 534) and the hexagon (523, 253, 235, 325, 352, 532) 

 passes into a triangle, while the adjacent hexagons do not change 

 in form. So we get fig. 18, where each vertex bears a triplet of 

 digits, of which the order of succession of the first and the second 

 is irrelevant, while e.g. 345 results from the coincidence of the 

 vertices 345 and 435 of fig. 11. In this figure the tT of vertex 

 import, remained unaltered, are recognized by the pi-operty that at 

 their vertices the same digit occurs under the first two of the three 

 digits, whilst the five other tT of body import lie in projection 

 symmetrically with these with respect to the centre. 



It may still be remarked that the centre of the figure can also 

 be found by dhiwing the tT of fig. 4 twice and by putting these 

 two tT with a difference of 36° in orientation in such a way upon 



