Answer:


One sees the secondary structure patter (Strand - Helix) 8 times repeated with two small extra helices 'on the top' (calling the direction in which the strands point the top). Strand 1 is in the barrel of strands followed by strand 2, strand 3, etc.
In the Netherlands little children play a knitting like game called 'punnikken' (Strickliesel for our German friends) that leads to a similar nearest-neighbour construct own secondary structure elements, but with punnikken it is in wool rather than strands and helices.
A series of points that you might/should have realized: 1 β-barrel: Barrel of parallel β-strands, with ring of α-helices around. 8 times βα secondary structure element. called barrel because it 'looks like' an old-fashion wooden beer barrel or a Dutch 'regenton'.
2 Following the chain one finds all the time, a beta going up, a short loop, an alpha going down, a short loop, and this eight times in a row.
3 The tunnel inside of TIM might seem open but is rather closely packed. It is often lined with polarresidues. In sugar cleaving enzymes you often find a series of negatively charged amino acids (mainly Asp, but also Glu; and normally one Asp binds a proton that is needed in the catalysis)
4 Actually, it is possible to connect the N- and the C- terminus in such proteins, and cut somewhere some loop, and still maintain a properly folding protein. This has been done experimentally by Kirchner in the early 90's already.
5 Most common motif in enzymes (amylases, chitinases, proteases, cellulases, isomerases), ca. 2000 enzymes known.
6 In those 2000 barrel structures always at least one of the catalytic site residues of the enzyme is found at the C-terminal end of a strand; either just in, or just C-terminally after a βstrand
7 In TIM in the active site one residue makes a contact with a loop in the other subunit. A monomer is not active, the dimer is the biologically active unit.
8 This is yet another example of the fact that structure is much more conserved than sequence. If you look at amylases versus chitinases: 2 of the active site amino acids are actually interchanged but the 3D structures are essentially identical!