Restricted tesselation types part 2

(This post is a continuation of a previous post. It will not make much sense except as a continuation of that post.)

IH34 is a restricted rhombus with 60 and 120 degree angles of Heesch type C3C3C3C3. All side are identical. It can be created using Tesselmaniac with template type CC6C6 and ignoring the C line. The example below is the vaguely S shaped figure. (In all of these examples, some lines have to be ignored or eliminated to get the desired tile.)

IH57 is a restricted parallelogram of Heesch type CCCC or TTTT. All sides have central-point rotation with opposite sides identical. It can be created using the Tesselmaniac template for TCTC and ignoring one of the C lines between tiles, the yellow line in the example below.

IH59 is a restricted rhombus of Heesch type G1G1G2G2 with all sides identical but without mirroring. The easiest way to get this tile in Tesselmaniac is with the CGG template, dropping the C sides. 

IH61 is a restricted square of Heesch type C4C4C4C4 with all sides identical. It can be created in Tesselmaniac using the CC4C4 and dropping the C section to unite the two segments.

IH62 is a square of Heesch type CCCC and also C4C4C4C4 with all sides identical. It can be created in Tesselmaniac with the template for C4C4C4C4 using only one set of the C4C4 pairs.

IH73 is a variant of IH61 with the further restriction that all sides are symmetrical around their middles. This cannot be exactly created in Tesselmaniac because Tesselmaniac does not have the drawing tools to line up points or segments exactly. Below is an approximation of the type.

These various special cases of Heesch types are mostly useful for generating abstract, geometrical shapes.

More information and more examples of these isohedral classes are available in Exploring Tessellations: A Journey through Heesch Types And Beyond. It is available from Amazon.