Symmetric tags

23) A surface bearing machine-readable coded data, the coded data being arranged in accordance with at least one layout having n-fold rotational symmetry about a center of rotation, where n is at least two, and having mirror symmetry, the layout including:

• (a) n identical first sub-layouts rotated 1/n revolutions apart about the center of rotation, and,
• (b) n identical second sub-layouts rotated 1/n revolutions apart about the center of rotation, each second sub-layout being a reflection of a corresponding one of the first sub-layouts, at least one sub-layout including:
• (i) rotation-indicating data that distinguishes that sub-layout from at least one other sub-layout;
• and,
• (ii) reflection-indicating data that distinguishes the reflection of that sub-layout from the reflection of a corresponding reflected sub-layout.

28) A method of generating an interface surface, the method including the steps of:

• (a) receiving user data in a printer;
• (b) generating machine-readable coded data incorporating the user data, the coded data being arranged in accordance with at least one layout having n-fold rotational symmetry about a center of rotation, where n is at least two, and having mirror symmetry, the layout including:
• (i) n identical first sub-layouts rotated 1/n revolutions apart about the center of rotation, and,
• (ii) n identical second sub-layouts rotated 1/n revolutions apart about the center of rotation, each second sub-layout being a reflection of a corresponding one of the first sub-layouts, at least one sub-layout including:
• (1) rotation-indicating data that distinguishes that sub-layout from at least one other sub-layout;
• and,
• (2) reflection-indicating data that distinguishes the reflection of that sub-layout from the reflection of a corresponding reflected sub-layout.
• (c) printing the coded data onto a surface.

31) A method of using a sensing device to read machine-readable coded data, the coded data being arranged in accordance with at least one layout having n-fold rotational symmetry about a center of rotation, where n is at least two, and having mirror symmetry, the layout including:

• (i) n identical first sub-layouts rotated 1/n revolutions apart about the center of rotation, and,
• (ii) n identical second sub-layouts rotated 1/n revolutions apart about the center of rotation, each second sub-layout being a reflection of a corresponding one of the first sub-layouts, at least one sub-layout including:
• (1) rotation-indicating data that distinguishes that sub-layout from at least one other sub-layout;
• and,
• (2) reflection-indicating data that distinguishes the reflection of that sub-layout from the reflection of a corresponding reflected sub-layout.
• (b) sensing at least one layout using the sensing device;
• (c) decoding the coded data of at least one of the sub-layouts of the sensed layout, thereby determining at least the rotation-indicating data of that sub-layout;
• and
• (d) using the rotation-indicating data to interpret the meaning of at least some of the coded data.

53) A method of using a sensing device to read machine-readable coded data, the coded data being arranged in accordance with at least one layout having n-fold rotational symmetry about a center of rotation, where n is at least two, the layout including n identical sub-layouts rotated 1/n revolutions apart about the center of rotation, each sub-layout encoding a codeword formed from a number of data elements, the sub-layout defining the position of the data elements, and including rotation-indicating data that distinguishes that sub-layout from at least one other sub-layout.

• (a) sensing at least one layout using the sensing device;
• (b) decoding the coded data of at least one of the sub-layouts of the sensed layout, thereby determining at least the rotation-indicating data of that sub-layout;
• and
• (c) using the rotation-indicating data to interpret the meaning of at least some of the coded data.