Pentiamond-Heptiamond Pair Pentagons

Introduction

A pentiamond is a plane figure formed by joining 5 equal equilateral triangles edge to edge. There are 4 pentiamonds:

A heptiamond is a plane figure formed by joining 7 equal equilateral triangles edge to edge. There are 24 heptiamonds:

Here I show the smallest known pentagonal (five-sided) polyiamonds that can be formed by copies of a pentiamond and a heptiamond, using at least one of each. If you find a smaller solution, please write.

Table

This table shows the number of cells in the smallest known solution for a given pentiamond and heptiamond. Colors indicate types of pentagons.

	7A	7B	7C	7D	7E	7F	7G	7H	7I	7J	7K	7L	7M	7N	7P	7Q	7R	7S	7T	7U	7V	7X	7Y	7Z
5I	37	17	17	17	34	41	17	19	17	49	22	12	12	29	47	17	37	31	22	99	90	49	37	39
5J	34	36	39	34	32	17	24	17	29	62	39	17	32	36	39	71	29	34	62	47	39	104	51	69
5Q	36	109	36	17	?	17	17	87	12	17	?	31	12	17	17	?	17	?	?	84	36	?	79	17
5U	?	?	?	?	189	?	60	105	19	?	?	17	60	?	?	?	?	?	?	?	?	?	?	?

12 Cells

17 Cells

19 Cells

22 Cells

24 Cells

29 Cells

31 Cells

32 Cells

34 Cells

36 Cells

37 Cells

39 Cells

41 Cells

47 Cells

49 Cells

51 Cells

60 Cells

62 Cells

69 Cells

71 Cells

79 Cells

84 Cells

87 Cells

90 Cells

99 Cells

104 Cells

105 Cells

109 Cells

189 Cells

Last revised 2025-03-08.

Back to Polyiamond and Polyming Tiling < Polyform Tiling < Polyform Curiosities

Col. George Sicherman [ HOME | MAIL ]

	7A	7B	7C	7D	7E	7F	7G	7H	7I	7J	7K	7L	7M	7N	7P	7Q	7R	7S	7T	7U	7V	7X	7Y	7Z
5I	37	17	17	17	34	41	17	19	17	49	22	12	12	29	47	17	37	31	22	99	90	49	37	39
5J	34	36	39	34	32	17	24	17	29	62	39	17	32	36	39	71	29	34	62	47	39	104	51	69
5Q	36	109	36	17	?	17	17	87	12	17	?	31	12	17	17	?	17	?	?	84	36	?	79	17
5U	?	?	?	?	189	?	60	105	19	?	?	17	60	?	?	?	?	?	?	?	?	?	?	?

	7A	7B	7C	7D	7E	7F	7G	7H	7I	7J	7K	7L	7M	7N	7P	7Q	7R	7S	7T	7U	7V	7X	7Y	7Z
5I	37	17	17	17	34	41	17	19	17	49	22	12	12	29	47	17	37	31	22	99	90	49	37	39
5J	34	36	39	34	32	17	24	17	29	62	39	17	32	36	39	71	29	34	62	47	39	104	51	69
5Q	36	109	36	17	?	17	17	87	12	17	?	31	12	17	17	?	17	?	?	84	36	?	79	17
5U	?	?	?	?	189	?	60	105	19	?	?	17	60	?	?	?	?	?	?	?	?	?	?	?

	7A	7B	7C	7D	7E	7F	7G	7H	7I	7J	7K	7L	7M	7N	7P	7Q	7R	7S	7T	7U	7V	7X	7Y	7Z
5I	37	17	17	17	34	41	17	19	17	49	22	12	12	29	47	17	37	31	22	99	90	49	37	39
5J	34	36	39	34	32	17	24	17	29	62	39	17	32	36	39	71	29	34	62	47	39	104	51	69
5Q	36	109	36	17	?	17	17	87	12	17	?	31	12	17	17	?	17	?	?	84	36	?	79	17
5U	?	?	?	?	189	?	60	105	19	?	?	17	60	?	?	?	?	?	?	?	?	?	?	?