Goblets, wine glasses, or chalices are easy to tessellate and if you search the Internet for images you should be able to find at least two ways in which the shape fits into a tiling pattern. Below is one of these ways.
The five-edged goblets are an example of isohedral class IH26. IH26 is the result of bisecting isohedral class IH17. If the straight bottom is considered an edge of central rotation, the pattern fits Heesch type TCTCC. If it is an edge of reflection, it is not a Heesch type.
If we slide alternate rows, each glass has six neighbors rather than the five in the pattern above.
When the six-edged goblets are centered over each other as in the image above, we have an example of isohedral class IH15, which simultaneously fits Heesch types TCCTCC, TCCTGG, and TG1G1TG2G2.
The other easy way to tessellate this shape is to stack them in the pattern below.
This arrangement is an example of isohedral class IH12 that simultaneously fits Heesch types TTTTTT and TG1G1TG2G2. Four of the edges are identically shaped.
All six edges can be identically shaped and the image still resembles a chalice or wine glass.
However, this shape can also be fit together in a different way, one that I have not found on the Internet.
It is an example of Heesch type TG1G1TG2G2 but not of TTTTTT. Can you find the TT pair?
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