Tiling a Regular Hexagon with Three Hexiamonds

A hexiamond is a plane figure formed by joining six equal equilateral triangles edge to edge.

Here I show the smallest known regular hexagons that can be tiled by copies of three hexiamonds, using at least one of each. Tilings in green, violet, and orange are known to be unique for the hexagon shown. If you find a smaller solution or solve an unsolved case, please write.

Table

The figures in this table tell the side lengths of the hexagons.

AEF 3AEH 6AEI ?AEL 2AEO 3AEP 5AES 4AEU 3AEV 4AEX ?
AFH 4AFI 3AFL 2AFO 3AFP 4AFS 5AFU 4AFV 4AFX 4AHI 3
AHL 3AHO 4AHP 5AHS 6AHU 4AHV 4AHX 6AIL 3AIO 4AIP 3
AIS 4AIU 3AIV 3AIX ?ALO 3ALP 3ALS 3ALU 2ALV 3ALX 4
AOP 4AOS 7AOU 5AOV 3AOX 6APS 4APU 3APV 4APX 5ASU 5
ASV 4ASX 6AUV 3AUX 4AVX 4EFH 4EFI 3EFL 3EFO 4EFP 3
EFS 4EFU 3EFV 4EFX 4EHI 4EHL 3EHO 4EHP 5EHS 6EHU 3
EHV 4EHX ?EIL 3EIO 3EIP 4EIS 4EIU 3EIV 4EIX ?ELO 2
ELP 4ELS 3ELU 2ELV 3ELX 5EOP 4EOS ?EOU 4EOV 4EOX 4
EPS 4EPU 3EPV 4EPX 5ESU 3ESV 3ESX ?EUV 3EUX 2EVX 4
FHI 3FHL 3FHO 4FHP 4FHS 4FHU 3FHV 4FHX 4FIL 3FIO 4
FIP 3FIS 3FIU 3FIV 3FIX 4FLO 3FLP 3FLS 4FLU 3FLV 3
FLX 4FOP 4FOS 5FOU 3FOV 3FOX 5FPS 4FPU 3FPV 4FPX 4
FSU 3FSV 4FSX 5FUV 4FUX 4FVX 4HIL 3HIO 3HIP 3HIS 3
HIU 3HIV 3HIX 5HLO 3HLP 3HLS 3HLU 2HLV 3HLX 4HOP 3
HOS 3HOU 3HOV 2HOX 5HPS 3HPU 3HPV 3HPX 5HSU 3HSV 2
HSX ?HUV 3HUX 4HVX 4ILO 3ILP 3ILS 3ILU 3ILV 3ILX 3
IOP 3IOS 4IOU 4IOV 3IOX 3IPS 3IPU 3IPV 3IPX 3ISU 3
ISV 3ISX 4IUV 3IUX 3IVX 3LOP 3LOS 6LOU 4LOV 3LOX 4
LPS 3LPU 3LPV 3LPX 4LSU 3LSV 3LSX 5LUV 3LUX 4LVX 4
OPS 3OPU 3OPV 3OPX 3OSU 5OSV 3OSX 5OUV 3OUX 5OVX 4
PSU 3PSV 3PSX 3PUV 3PUX 3PVX 4SUV 3SUX 3SVX 4UVX 4

Side 2

Side 3

Side 4

Side 5

Side 6

Side 7

Last revised 2025-12-27.


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Col. George Sicherman [ HOME | MAIL ]