type ${\Phi}$ with apartments in one to one correspondence with the apartments of $X$.

The remainder of the present paper is paper is organized as follows. {#the-remainder-of-the-present-paper-is-paper-is-organized-as-follows. .unnumbered}
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In the next section we will give a combinatorial definition of parallelism of Weyl simplices. Using this we prove the existence of the spherical building at infinity using axioms (A1) to (A4), only.

The rest of the paper, Sections \[Sec\_infinity\] to \[Sec\_A6’\], need not be read sequentially. There we prove one after another the implications of \[MainThm\] as shown in the diagram on page . The only sections which are better read in a row are Sections \[Sec\_retractions\] to \[Sec\_A5\]. Otherwise the best possible strategy might be to pick ones favorite inclusion and read the sections needed for its proof. We did already say, after stating the main theorem in the previous subsection, where to find what.

The building at infinity {#Sec_infinity}
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Any simplicial affine building has an associated spherical building at infinity. Most of the constructions of the building at infinity found in the literature, such as the one in [@Parreau] or [@Brown; @AB] for example, heavily rely on the metric structure of the affine building. Bennett’s [@Bennett] proof 