Catalog of the 81 types

Each figure shows a patch of the type, with the tile colors of the type; the middle tile is amber. The page is generated from the type data when the documentation is built. So that types of the same default shape can be told apart, the figures do not use the default parameters and straight edges. Each parameter is moved 40 percent of the way from its default to the nearer finite end of its safe range (by 0.15 if both ends are infinite), and every edge of shape J (free), U (mirror symmetric) or S (rotation symmetric) has a fixed curve of that shape (a wave, a bump, an S), and edges with different edge shape ids get different curves. Edges of shape I stay straight. If the prototile is not valid, the parameter step and the curve heights are halved, up to four times; the figure then falls back to the default value or to a straight edge. The figures illustrate the symmetry of the type, not a recommended shape. Aspects is the number of tiles per lattice cell, Parameters the number of free parameters, Edges the shape of each edge of the prototile (I straight, J free curve, U mirror symmetric, S rotation symmetric) and Edge ids the number of distinct edge shape ids, which is the number of curves a tiling can carry. Reflections says whether some aspects are mirror images. find_types selects types by these properties.

Triangles

Tiling	Type	Aspects	Parameters	Edges	Edge ids	Reflections
	IH38	6	0	J I J	2	yes
	IH39	6	0	J S J	2	no
	IH40	6	0	I I I	2	no
	IH77	12	0	I I I	3	yes
	IH78	4	1	I S I	3	yes
	IH79	4	0	J S J	2	no
	IH81	8	0	J I J	2	yes
	IH82	4	0	I I I	2	no
	IH83	2	1	J J I	2	yes
	IH84	2	2	S S S	3	no
	IH85	4	2	I S S	3	yes
	IH86	4	1	J J S	2	yes
	IH88	6	0	J J S	2	no
	IH90	2	0	S S S	1	no
	IH91	2	1	S S I	2	no
	IH93	2	0	I I I	1	no

Quadrilaterals

Tiling	Type	Aspects	Parameters	Edges	Edge ids	Reflections
	IH30	6	1	J I I J	3	yes
	IH31	6	0	J J J J	2	no
	IH32	6	0	I I I I	2	yes
	IH33	3	0	J J J J	2	no
	IH34	3	0	J J J J	1	no
	IH36	3	0	J J J J	1	yes
	IH37	3	0	I I I I	1	yes
	IH41	1	2	J J J J	2	no
	IH42	2	2	J I J I	3	yes
	IH43	2	2	J J J J	2	yes
	IH44	2	2	J J J J	2	yes
	IH45	2	2	J I J I	3	yes
	IH46	2	4	S S S S	4	no
	IH47	2	2	J S J S	3	no
	IH49	4	3	I S I S	4	yes
	IH50	4	2	J I J S	3	yes
	IH51	4	3	J S J S	3	yes
	IH52	4	1	J J J J	2	yes
	IH53	4	3	J J S S	3	yes
	IH54	4	2	I I I S	4	yes
	IH55	4	0	J J J J	2	no
	IH56	8	1	J J I I	3	yes
	IH57	1	2	S S S S	2	no
	IH58	2	2	S I S I	2	yes
	IH59	2	1	J J J J	1	yes
	IH61	2	0	J J J J	1	no
	IH62	1	0	S S S S	1	no
	IH64	1	1	U I U I	2	no
	IH66	2	1	U S U S	2	no
	IH67	2	2	S I S I	3	no
	IH68	1	1	J J J J	1	no
	IH69	2	2	S S S S	2	no
	IH71	4	0	J J J J	1	no
	IH72	1	1	I I I I	2	no
	IH73	2	0	U U U U	1	no
	IH74	1	1	S S S S	1	no
	IH76	1	0	I I I I	1	no

Pentagons

Tiling	Type	Aspects	Parameters	Edges	Edge ids	Reflections
	IH21	6	2	S J J J J	3	no
	IH22	2	3	J J J I J	3	yes
	IH23	2	4	S S J S J	4	no
	IH24	4	4	S S J I J	4	yes
	IH25	4	3	J J J S J	3	yes
	IH26	2	2	S S I I I	3	no
	IH27	4	3	S J J J J	3	yes
	IH28	4	2	S J J J J	3	no
	IH29	4	1	I J J J J	2	yes

Hexagons

Tiling	Type	Aspects	Parameters	Edges	Edge ids	Reflections
	IH1	1	4	J J J J J J	3	no
	IH2	2	4	J J J J J J	3	yes
	IH3	2	4	J J J J J J	3	yes
	IH4	2	6	S J S S J S	5	no
	IH5	4	5	S J J J J S	4	yes
	IH6	4	5	S J S J J J	4	yes
	IH7	3	2	J J J J J J	3	no
	IH8	1	4	S S S S S S	3	no
	IH9	2	3	S J J S J J	2	yes
	IH10	1	0	J J J J J J	1	no
	IH11	1	0	S S S S S S	1	no
	IH12	1	2	U J J U J J	2	no
	IH13	2	3	U S S U S S	3	no
	IH14	1	2	J I J J I J	2	no
	IH15	2	3	S I S S I S	3	no
	IH16	3	1	I J J J J I	2	yes
	IH17	1	2	I S S I S S	2	no
	IH18	1	0	U U U U U U	1	no
	IH20	1	0	I I I I I I	1	no