Tiling Isosceles Trapezia with Scaled Pentabolo Pairs

Introduction

A scaled pentabolo is a pentabolo whose size may be altered without changing its shape. In geometric terms, it is a family of similar pentaboloes.

A trapezium (trapezoid in Canada and the U.S.) is a plane figure with four sides, two of them parallel. A isosceles trapezium is a trapezium whose two non-parallel sides have the same length.

For every pair of scaled pentaboloes, I show an isosceles trapezium that they can tile, using at least one of each, and using as few tiles as known to be possible. If you find a smaller solution or solve an unsolved case, please write.

Table of Results

Theoretically, scaled pentabolo 24 and any other scaled pentabolo can together tile an isosceles trapezium. I do not have tilings for all such pairs of scaled pentaboloes.

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
2	?	•	?	?	?	?	?	5	4	?	?	?	4	?	?	?	?	?	?	?	?	?	?	26	?	?	3	?	?	8
8	18	5	?	?	?	36	?	•	4	?	20	4	?	?	4	?	3	?	?	?	14	?	?	?	?	79	4	4	7	?
9	8	4	7	6	8	6	7	4	•	8	8	8	6	6	5	7	9	5	7	8	4	8	6	5	6	4	3	4	5	3
24	?	26	52	3	?	23	?	?	5	?	26	26	?	?	4	42	23	45	66	34	12	?	?	•	?	66	16	43	17	42
26	?	?	14	?	?	6	?	79	4	?	6	?	4	?	7	?	?	35	41	?	25	?	?	66	?	•	5	?	?	?
27	5	3	7	21	18	18	20	4	3	8	7	7	9	37	7	32	29	31	51	25	4	33	48	16	38	5	•	7	5	8
30	9	8	45	8	?	8	?	?	3	?	8	8	?	?	3	21	?	64	16	?	22	?	?	42	?	?	8	28	?	•

Navigation

3 Tiles

4 Tiles

5 Tiles

6 Tiles

7 Tiles

8 Tiles

9 Tiles

12 Tiles

14 Tiles

16 Tiles

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20 Tiles

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22 Tiles

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25 Tiles

26 Tiles

28 Tiles

29 Tiles

31 Tiles

32 Tiles

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35 Tiles

36 Tiles

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41 Tiles

42 Tiles

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45 Tiles

48 Tiles

51 Tiles

52 Tiles

64 Tiles

66 Tiles

79 Tiles

Last revised 2025-09-28.