The vertices are assigned the blue labels, v[n]; note the 'wraparound' and absence of 'v1'and 'v12' where the graphic would otherwise appear cluttered.

By assigning values from 1 to 20 to each of the capital letters A through T determine a layout whereby the vertex sums are either 52 or 53 in equal number;

__let__A=1.

Note that a 'vertex sum' is the total of the values assigned to the faces which converge at a given vertex.

__Question__:

Can values be assigned such that the vertex sums can form an arithmetical progression?