Minimal Oddities for the L Tetracube

Introduction

A tetracube is a solid made of 4 equal cubes joined face to face. There are 8 different tetracubes, distinguishing mirror images. The L tetracube is shaped like the letter L:

A polyform oddity is a shape with even symmetry formed by joining an odd number of copies of a polyform.

Polycubes can belong to any of 33 symmetry classes, including asymmetry; see Polycube Symmetries. Of these symmetry classes, 31 have even order and can be symmetries of oddities.

Here I show minimal oddities for the L tetracube that belong to every even symmetry class. If you find a smaller example for any symmetry class, please write.

For pentacubes, see Polycube Oddities.

Solutions

The symmetry codes are those of W. F. Lunnon; see Polycube Symmetries. The order of a symmetry is shown in parentheses next to its code. After that appears the number of copies of the L tetracube. An asterisk means that the figure is unique for its class and number of tiles.

C4(2) 3 B6(2) 3 K6(2) 3 F5(2) 3

E4(2) 1* A12(4) 5 J10(4) 5 BC10(4) 5*

BB10(4) 5 CK6(4) 5 BE4(4) 5 CE3(4) 3

BF6(4) 5 EE4(4) 3* CD10(6) 3* FF4(6) 3*

H12(6) 3* AB16(8) 7 EF6(8) 5* BFF8(8) 7*

CJ6(8) 7 AE8(8) 7* EFF7(8) 7* EEE6(8) 5*

BD34(12) 9* CF6(12) 3* BBC2(16) 7* R56(24) 27

CCC20(24) 21 DEE25(24) 9* G1(48) 27

Acknowledgment

Thanks to Joyce Michel for reporting errors in this page and suggesting an emendation to the text.

Last revised 2026-05-30.

Back to Polycube Oddities < Polyform Oddities < Polyform Curiosities

Col. George Sicherman [ HOME | MAIL ]

C4(2) 3	B6(2) 3	K6(2) 3	F5(2) 3

E4(2) 1*	A12(4) 5	J10(4) 5	BC10(4) 5*

BB10(4) 5	CK6(4) 5	BE4(4) 5	CE3(4) 3

BF6(4) 5	EE4(4) 3*	CD10(6) 3*	FF4(6) 3*

H12(6) 3*	AB16(8) 7	EF6(8) 5*	BFF8(8) 7*

CJ6(8) 7	AE8(8) 7*	EFF7(8) 7*	EEE6(8) 5*

BD34(12) 9*	CF6(12) 3*	BBC2(16) 7*	R56(24) 27

CCC20(24) 21	DEE25(24) 9*	G1(48) 27