Minimal Oddities for the P Pentacube

Introduction

A pentacube is a solid made of five equal cubes joined face to face. There are 29 different pentacubes, distinguishing mirror images. The P pentacube is shaped like the letter P:

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 P pentacube that belong to every even symmetry class. If you find a smaller example for any symmetry class, please write.

For other 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 P pentacube. An asterisk means that the figure is unique for its number of tiles.

C4(2) 3 B6(2) 5 CF6(2) 5 F5(2) 3

E4(2) 1* A12(4) 5* J10(4) 7 BC10(4) 7

BB10(4) 9 CK6(4) 5* BE4(4) 5* CE3(4) 3

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

H12(6) 5* AB16(8) 9 EF6(8) 5* BFF8(8) 7

CJ6(8) 9 AE8(8) 9 EFF7(8) 7 EEE6(8)

BD34(12) 17 DF6(12) 5* BBC2(16) 9* R56(24) 25*

CCC20(24) 17* DEE25(24) 25* G1(48) 25*

Last revised 2024-05-12.

Back to Polyform Oddities < Polyform Curiosities

Col. George Sicherman [ HOME | MAIL ]

C4(2) 3	B6(2) 5	CF6(2) 5	F5(2) 3

E4(2) 1*	A12(4) 5*	J10(4) 7	BC10(4) 7

BB10(4) 9	CK6(4) 5*	BE4(4) 5*	CE3(4) 3

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

H12(6) 5*	AB16(8) 9	EF6(8) 5*	BFF8(8) 7

CJ6(8) 9	AE8(8) 9	EFF7(8) 7	EEE6(8)

BD34(12) 17	DF6(12) 5*	BBC2(16) 9*	R56(24) 25*

CCC20(24) 17*	DEE25(24) 25*	G1(48) 25*