Ghyka lists 10 of them with 2 or 3 vertex types, calling them semiregular polymorph partitions.[1]
Plate XXVII No. 12 4.6.12 3.4.6.4
No. 13 3.4.6.4 3.3.3.4.4
No. 13 bis. 3.4.4.6 3.3.4.3.4
No. 13 ter. 3.4.4.6 3.3.3.4.4
Plate XXIV No. 13 quatuor. 3.4.6.4 3.3.4.3.4
No. 14 33.42 36
Plate XXVI No. 14 bis. 3.3.4.3.4 3.3.3.4.4 36
No. 14 ter. 33.42 36
No. 15 3.3.4.12 36
Plate XXV No. 16 3.3.4.12 3.3.4.3.4 36
Steinhaus's list (1969)
Steinhaus gives 5 examples of non-homogeneous tessellations of regular polygons beyond the 11 regular and semiregular ones.[2] (All of them have 2 types of vertices, while one is 3-uniform.)
2-uniform
3-uniform
Image 85 33.42 3.4.6.4
Image 86 32.4.3.4 3.4.6.4
Image 87 3.3.4.12 36
Image 89 33.42 32.4.3.4
Image 88 3.12.12 3.3.4.12
Critchlow's list (1970)
Critchlow identifies 14 demi-regular tessellations, with 7 being 2-uniform, and 7 being 3-uniform.
He codes letter names for the vertex types, with superscripts to distinguish face orders. He recognizes A, B, C, D, F, and J can't be a part of continuous coverings of the whole plane.
Ghyka, M. The Geometry of Art and Life, (1946), 2nd edition, New York: Dover, 1977.
Keith Critchlow, Order in Space: A design source book, 1970, pp. 62–67
Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN0-486-23729-X. pp. 35–43
Steinhaus, H. Mathematical Snapshots 3rd ed, (1969), Oxford University Press, and (1999) New York: Dover
