A barrel die is an uncommon type of die

Dice

A die is a small throwable object with multiple resting positions, used for generating random numbers...

 used most often by players of role playing games and wargames

Wargaming

A wargame is a strategy game that deals with military operations of various types, real or fictional. Wargaming is the hobby dedicated to the play of such games, which can also be called conflict simulations, or consims for short. When used professionally to study warfare, it is generally known as...

.
It is similar to rolling logs.

Its shape is roughly cylindrical

Cylinder (geometry)

A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder...

 with between four and twenty flattened triangular facets, each numbered. Each triangular face alternates in alignment about 180 degrees. The two ends of the cylindroid are formed by half as many triangular facets as there are numbered faces, and are arranged so that it is impossible for the die to stop on one of its 'ends'.

There are six versions: 4, 6, 8, 10, 12, and 20 sides. They all have triangular faces except the 4 sided one, having rectangular faces much like a dreidel

Dreidel

A dreidel is a four-sided spinning top, played with during the Jewish holiday of Hanukkah.Each side of the dreidel bears a letter of the Hebrew alphabet:נ ,ג ,ה ,ש ,...

, and is also used in the traditional games daldøs

Daldøs

Daldøs [dal'døs] is a running-fight board game only known from a few coastal locations in Scandinavia, where its history can be traced back to around 1800. The game is notable for its unusual four-sided rolling-pin style dice . In Denmark it is known as daldøs in Northern and Western Jutland , and...

 and dayakattai

Dayakattai

Dayakattai is an Indian dice game played by two to four people. It is very similar to Parchesi in terms of gameplay. Typically all players start with six coins/chips at a 'home' in the center of the board. They each take turns rolling the Dayakattai, a pair of dice that are shaped like long...

. The 4 sided barrel die is easier to roll than the normal tetrahedral d4 used in most role-playing games.

A barrel die is rolled longitudinally so that one of the numbered faces comes to rest on top.

The cricket game "Owzthat

Owzthat

Owzthat is a dice based cricket simulation. In its non-commercial form it is often called Pencil Cricket as in pre-war Britain 6 sided pencils, shaved back to bare wood, with the numbers and words written on them were used...

" (relatively) popular in the 1960s-70s in England used barrel dice which were essentially short lengths of hexagonal bar (i.e. with 6 rectangular faces). The dice were rolled, rather than thrown, and there were no special precautions to prevent the dice landing or stopping end-on