Tiling Right 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 right trapezium is a trapezium with one side perpendicular to the parallel sides.

For every pair of scaled pentaboloes, I show a 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 a 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	?	?	?	2	?	?	?	?	?	?	?	?	?	?	13	?	?	?	?	?	4
8	?	?	?	?	?	?	?	•	3	?	15	?	?	?	2	?	?	?	?	?	22	?	?	?	?	?	?	?	4	?
9	7	5	6	5	7	4	6	3	•	7	6	6	5	5	4	5	7	4	5	7	3	6	5	3	5	3	2	5	4	2
24	?	13	32	10	?	13	?	?	3	?	13	13	?	?	2	23	17	?	33	17	18	?	?	•	?	33	12	30	11	89
26	?	?	17	?	?	3	?	?	3	?	18	?	2	?	19	?	?	?	?	?	19	?	?	33	?	•	?	?	?	?
27	?	?	?	?	50	21	35	?	2	?	25	?	10	?	10	?	?	?	?	?	2	?	?	12	?	?	•	?	8	8
30	8	4	27	4	?	4	?	?	2	?	4	4	?	?	6	22	?	?	8	?	23	?	?	89	?	?	8	?	?	•

2 Tiles

3 Tiles

4 Tiles

5 Tiles

6 Tiles

7 Tiles

8 Tiles

10 Tiles

11 Tiles

12 Tiles

13 Tiles

15 Tiles

17 Tiles

18 Tiles

19 Tiles

21 Tiles

22 Tiles

23 Tiles

25 Tiles

27 Tiles

30 Tiles

32 Tiles

33 Tiles

35 Tiles

50 Tiles

89 Tiles

Last revised 2025-09-20.