While working on Blox, I wrote a module that functioned essentially as a beefed-up NormalId enum. It has more intuitive constants and plenty of useful properties for you to use, as well as methods of converting to and from other data types.
The code is below, feel free to use it in your own projects 
--[[
Facing
a better enum for working with faces
by Elttob
--]]
local Facing = {}
Facing.__index = Facing
local normalIDOpposites = {
[Enum.NormalId.Top] = Enum.NormalId.Bottom,
[Enum.NormalId.Bottom] = Enum.NormalId.Top,
[Enum.NormalId.Front] = Enum.NormalId.Back,
[Enum.NormalId.Back] = Enum.NormalId.Front,
[Enum.NormalId.Left] = Enum.NormalId.Right,
[Enum.NormalId.Right] = Enum.NormalId.Left
}
local normalIDToFacingMap = {}
local facingIDToFacingMap = {}
Facing.allFacings = {}
local function newFacing(normalID, facingID)
local obj = setmetatable({}, Facing)
obj.normalID = normalID
obj.facingID = facingID
normalIDToFacingMap[normalID] = obj
facingIDToFacingMap[facingID] = obj
Facing.allFacings[#Facing.allFacings + 1] = obj
return obj
end
function Facing.fromNormalID(normalID)
return normalIDToFacingMap[normalID]
end
function Facing.fromFacingID(facingID)
return facingIDToFacingMap[facingID]
end
Facing.TOP = newFacing(Enum.NormalId.Top, 1)
Facing.BOTTOM = newFacing(Enum.NormalId.Bottom, 2)
Facing.FRONT = newFacing(Enum.NormalId.Front, 4)
Facing.BACK = newFacing(Enum.NormalId.Back, 8)
Facing.LEFT = newFacing(Enum.NormalId.Left, 16)
Facing.RIGHT = newFacing(Enum.NormalId.Right, 32)
Facing.UP = Facing.TOP
Facing.DOWN = Facing.BOTTOM
Facing.X_POSITIVE = Facing.RIGHT
Facing.X_NEGATIVE = Facing.LEFT
Facing.Y_POSITIVE = Facing.UP
Facing.Y_NEGATIVE = Facing.DOWN
Facing.Z_POSITIVE = Facing.BACK
Facing.Z_NEGATIVE = Facing.FRONT
for _, facing in pairs(normalIDToFacingMap) do
facing.direction = Vector3.FromNormalId(facing.normalID)
facing.opposite = Facing.fromNormalID(normalIDOpposites[facing.normalID])
facing.axis = Vector3.new(
facing.direction.X ~= 0 and 1 or 0,
facing.direction.Y ~= 0 and 1 or 0,
facing.direction.Z ~= 0 and 1 or 0
)
end
return Facing
Module API
Facing.TOP
The Facing object for the positive Y direction.
Aliases: UP, Y_POSITIVE
Facing.BOTTOM
The Facing object for the negative Y direction.
Aliases: DOWN, Y_NEGATIVE
Facing.FRONT
The Facing object for the negative Z direction.
Aliases: Z_NEGATIVE
Facing.BACK
The Facing object for the positive Z direction.
Aliases: Z_POSITIVE
Facing.LEFT
The Facing object for the negative X direction.
Aliases: X_NEGATIVE
Facing.RIGHT
The Facing object for the positive Xdirection.
Aliases: X_POSITIVE
Facing.allFacings
Stores references to all 6 Facing objects (up, down, left, right, front, back) as a list.
The order of the list is undefined, and shouldn’t be relied upon.
Facing.fromNormalID(Enum.NormalId normalID)
Returns the Facing object for the given NormalId.
Facing.fromFacingID(int facingID)
Returns the Facing object for the given integer ID, corresponding to the facingID property of the Facing object.
Facing object API
Facing.normalID
Stores the NormalId enum for this Facing object.
Facing.facingID
Stores an integer ID for this Facing object, useful for combining and serialising Facing objects.
Facing.direction
Stores a Vector3 direction for this Facing object (normal to the face represented by this object)
Facing.opposite
Stores the Facing object pointing in the opposite direction of this Facing object.
Facing.axis
Stores a Vector3 representing the axis this Facing object is oriented along.
For example, Facing.X_POSITIVE and Facing.X_NEGATIVE have axis values of (1, 0, 0)