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<blockquote data-quote="calronmoonflower" data-source="post: 6704862" data-attributes="member: 6750045">Hypercubes Made EasyHypercubes Made Easy, or Tesseracts Make My Head Explode :headexploI first found the idea of a hypercube in the Dragon Compendium. This article expands on that article’s both a fascinating and confusing idea. Here I will describe a hypercube and try to make a cheat sheet that lets you use a hypercube with out the headaches. What Is a Hypercube? It's a mathematical concept that doesn't work in a 3-D environment. A normal cube can be made of twenty seven small uniform cubes. A hypercube, however, is made from only eight identical cubes? Fitting only eight cubes in a space meant for twenty seven requires a warping of space. Removing the extra cube changes how you move through the area and makes it very complicated to use in game.How to Draw a HypercubeDraw a big cube with a smaller cube inside, with all plains facing the same directions. Connecting the corners of the two cubes forms a diagram of a hypercube. You should be able to see seven distinct areas within the cube. Despite the trapezoid shapes all represent an identical cube. Where is the eighth cube? If you are like me you won't see the eighth cube just looking at the diagram. The eighth cube is the outside of the diagram. It forms another identical cube. The parts of a hypercube as far as I can tell are the inner cube, the outer cubes and the outside cube. I'm sure these have proper scientific names, but I don't know them and using them will not be necessary to use a hypercube in a D&amp;D game.Gravity in a HypercubeWithin the structure of a hypercube gravity becomes subjective. The &quot;floor&quot; that you are standing on is down. As you travel between the cubes down changes allowing you to walk on the wall and ceiling meaning that each of the 8 cubes has 6 surfaces that you can walk on for a total of 48 surfaces.The Outer CubesThe outer cubes make an interesting way to travel. When walking (or climbing) from one of the outer cubes to another you reoriented so down is a different way. If you are walking between them then you stay on the same plain (see the diagram), but if you climb the plain you are on increases by 1, but skips 1 and 6 when it rolls over. When you descend in number reduce, but also skip 1 and 6.Diagrams of the Outer RoomsI based the diagram up d6’s, but all the number do not match up when up into this form. I have made the changes, but it you build your own 3-D model of d6’s you will need to renumber some sides. These diagrams can also be a guild for building individual rooms based upon the cubes.[code]Outer Cubes Guide&nbsp; &nbsp; Individual Cubes&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Cube A&nbsp; cube B&nbsp; &nbsp; Cube C&nbsp;&nbsp; Cube D&nbsp; &nbsp;&nbsp; Cube E&nbsp;&nbsp; Cube F&nbsp;&nbsp; g&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3&nbsp; &nbsp; &nbsp;&nbsp; 4&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 1&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 6&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 4&nbsp; &nbsp; &nbsp; &nbsp; 4&nbsp;&nbsp; |&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; |&nbsp; &nbsp; &nbsp;&nbsp; |&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; |&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; |&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; |&nbsp; &nbsp; &nbsp; &nbsp; |&nbsp;&nbsp; f&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1-2-6-5&nbsp;&nbsp; 1-2-6&nbsp; &nbsp;&nbsp; 2-3-5-4&nbsp;&nbsp; 2-4-5-3&nbsp;&nbsp; 6-5-1-2&nbsp; 2-1-5-6&nbsp;&nbsp; |&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; |&nbsp; &nbsp; &nbsp;&nbsp; |&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; |&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; |&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; |&nbsp; &nbsp; &nbsp; &nbsp; |&nbsp;b-a-e&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 4&nbsp; &nbsp; &nbsp;&nbsp; 3&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 6&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 1&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 3&nbsp; &nbsp; &nbsp; &nbsp; 3&nbsp;&nbsp; |&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; |&nbsp;&nbsp; d&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 5[/code]This diagram is the best that I can do, and it contains a flaw. The floors extended from the by two - from the bottom (center number) do not match up. The 3 and 2 squares of cubes D and E do not match up properly. Keep this in mind when traveling between the floors. I'm sure there exists a way to align all the number correctly, but that is beyond me.The Inner Cube. A.K.A. Cube GThe floors marked 6 surround the inner cube. I suggest that you use the outer cubes to guide you through the inner cube. If you fold the diagram for the outer cubes diagram to look like a d6 you will end up with a guide for the inner cube. Note that unlike traveling to and from the inner you are not reoriented like you do when you travel between the outer cubes.The Outside Cube A.K.A Cube HWhere is cube H on the diagram? Each 1 leads to cube H. On the Outer cube guide cube H is the outside of the diagram. Like cube G you are not reoriented when you enter and exit cube H. The outer cube guide can also be used to guide you through cube H, however, you must fold it the other direct, with the letters on the inside.Stairs and DoorsTo fully connect every cube to all those around it each floor needs four doors and every wall needs four flights of stairs. This adds up to 256? total doors and flights of stairs. Making the stairs double sided will reduce the number to 128, but they will be two on every surface. Notice that doors will also be on every surface, so it is possible to open a door and drop down to the cube below.Keeping Track of OrientationThis is simpler that it sounds when using the diagram above. Keep a d6 for ever PC and place the proper number up and make sure they are on the right floor of each cube.One Mean Trick and a Big HeadacheIf you align the door so you must stand on a closed door to open another can really be hard on the PC in a hypercube, but remember you will need to keep track of all 256 doors!Entering a HypercubeDragon Compendium suggested that to enter a hypercube you should close all the doors on the same cube that exists on the cube and rest of the world. I suggest instead a one-way door. Then a character passes through this door they leave the universe and become trapped in the hypercube. If you allow the inside of the hypercube to be visible from the outside a character looking back would see another cube instead of the room that they came from. Another person on the outside would be able to see them and they would seem to disappear as the walked back the way they can and ended up.Exiting a HypercubeEvery direction within a hypercube leads to another part of the hypercube. This means there is no physical connection between a hypercube and the outside world. The only solution is a magic exit. It can be as the Dragon Compendium suggested and be a magic item that allows you to access the outside world be one of the door. I suggest that you make the item so it cannot leave the hypercube so characters to not become trapped. Another exit possibility is the teleport spell, or a teleportation device within the hypercube. You might even force the PCs to use teleport (or if you rule a hypercube a demi-plane, Plane Shift).Cube Space an Alternate Use of Cube HInstead of cube H being a room inside the hypercube you may have it be a free floating cube (same size as the other cubes) with space outside. Beyond that you may have the other side of the cube (in this case PCs might see themselves standing on other cubes) or absolute nothingness. In the case of nothingness you should not be able to enter that area as it has no space.</blockquote>

[QUOTE="calronmoonflower, post: 6704862, member: 6750045"] [b]Hypercubes Made Easy[/b] Hypercubes Made Easy, or Tesseracts Make My Head Explode :headexplo I first found the idea of a hypercube in the Dragon Compendium. This article expands on that article’s both a fascinating and confusing idea. Here I will describe a hypercube and try to make a cheat sheet that lets you use a hypercube with out the headaches. What Is a Hypercube? It's a mathematical concept that doesn't work in a 3-D environment. A normal cube can be made of twenty seven small uniform cubes. A hypercube, however, is made from only eight identical cubes? Fitting only eight cubes in a space meant for twenty seven requires a warping of space. Removing the extra cube changes how you move through the area and makes it very complicated to use in game. How to Draw a Hypercube Draw a big cube with a smaller cube inside, with all plains facing the same directions. Connecting the corners of the two cubes forms a diagram of a hypercube. You should be able to see seven distinct areas within the cube. Despite the trapezoid shapes all represent an identical cube. Where is the eighth cube? If you are like me you won't see the eighth cube just looking at the diagram. The eighth cube is the outside of the diagram. It forms another identical cube. The parts of a hypercube as far as I can tell are the inner cube, the outer cubes and the outside cube. I'm sure these have proper scientific names, but I don't know them and using them will not be necessary to use a hypercube in a D&D game. Gravity in a Hypercube Within the structure of a hypercube gravity becomes subjective. The "floor" that you are standing on is down. As you travel between the cubes down changes allowing you to walk on the wall and ceiling meaning that each of the 8 cubes has 6 surfaces that you can walk on for a total of 48 surfaces. The Outer Cubes The outer cubes make an interesting way to travel. When walking (or climbing) from one of the outer cubes to another you reoriented so down is a different way. If you are walking between them then you stay on the same plain (see the diagram), but if you climb the plain you are on increases by 1, but skips 1 and 6 when it rolls over. When you descend in number reduce, but also skip 1 and 6. Diagrams of the Outer Rooms I based the diagram up d6’s, but all the number do not match up when up into this form. I have made the changes, but it you build your own 3-D model of d6’s you will need to renumber some sides. These diagrams can also be a guild for building individual rooms based upon the cubes. [code]Outer Cubes Guide Individual Cubes Cube A cube B Cube C Cube D Cube E Cube F g 3 4 1 6 4 4 | | | | | | | f 1-2-6-5 1-2-6 2-3-5-4 2-4-5-3 6-5-1-2 2-1-5-6 | | | | | | | b-a-e 4 3 6 1 3 3 | | d 5[/code] This diagram is the best that I can do, and it contains a flaw. The floors extended from the by two - from the bottom (center number) do not match up. The 3 and 2 squares of cubes D and E do not match up properly. Keep this in mind when traveling between the floors. I'm sure there exists a way to align all the number correctly, but that is beyond me. The Inner Cube. A.K.A. Cube G The floors marked 6 surround the inner cube. I suggest that you use the outer cubes to guide you through the inner cube. If you fold the diagram for the outer cubes diagram to look like a d6 you will end up with a guide for the inner cube. Note that unlike traveling to and from the inner you are not reoriented like you do when you travel between the outer cubes. The Outside Cube A.K.A Cube H Where is cube H on the diagram? Each 1 leads to cube H. On the Outer cube guide cube H is the outside of the diagram. Like cube G you are not reoriented when you enter and exit cube H. The outer cube guide can also be used to guide you through cube H, however, you must fold it the other direct, with the letters on the inside. Stairs and Doors To fully connect every cube to all those around it each floor needs four doors and every wall needs four flights of stairs. This adds up to 256? total doors and flights of stairs. Making the stairs double sided will reduce the number to 128, but they will be two on every surface. Notice that doors will also be on every surface, so it is possible to open a door and drop down to the cube below. Keeping Track of Orientation This is simpler that it sounds when using the diagram above. Keep a d6 for ever PC and place the proper number up and make sure they are on the right floor of each cube. One Mean Trick and a Big Headache If you align the door so you must stand on a closed door to open another can really be hard on the PC in a hypercube, but remember you will need to keep track of all 256 doors! Entering a Hypercube Dragon Compendium suggested that to enter a hypercube you should close all the doors on the same cube that exists on the cube and rest of the world. I suggest instead a one-way door. Then a character passes through this door they leave the universe and become trapped in the hypercube. If you allow the inside of the hypercube to be visible from the outside a character looking back would see another cube instead of the room that they came from. Another person on the outside would be able to see them and they would seem to disappear as the walked back the way they can and ended up. Exiting a Hypercube Every direction within a hypercube leads to another part of the hypercube. This means there is no physical connection between a hypercube and the outside world. The only solution is a magic exit. It can be as the Dragon Compendium suggested and be a magic item that allows you to access the outside world be one of the door. I suggest that you make the item so it cannot leave the hypercube so characters to not become trapped. Another exit possibility is the teleport spell, or a teleportation device within the hypercube. You might even force the PCs to use teleport (or if you rule a hypercube a demi-plane, Plane Shift). Cube Space an Alternate Use of Cube H Instead of cube H being a room inside the hypercube you may have it be a free floating cube (same size as the other cubes) with space outside. Beyond that you may have the other side of the cube (in this case PCs might see themselves standing on other cubes) or absolute nothingness. In the case of nothingness you should not be able to enter that area as it has no space. [/QUOTE]

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