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 Pentacube Oddities with Full Symmetry and its links to other pentacube oddity pages.

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