241 lines
15 KiB
Plaintext
241 lines
15 KiB
Plaintext
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| TTTTTTT H H EEEEEEE |
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| T H H E |
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| T H H E |
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| T HHHHHHH EEEEE |
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| T H H E |
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| T H H E |
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| T H H EEEEEEE |
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| PPPPPP Y Y RRRRRR A M M III X X |
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| P P Y Y R R A A MM MM I X X |
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| P P Y Y R R A A M M M M I X X |
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| PPPPPP Y RRRRRR AAAAAAA M M M I X |
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| P Y R R A A M M I X X |
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| P Y R R A A M M I X X |
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| P Y R R A A M M III X X |
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| A Solution to the Pyramix |
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| u |
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| /|\ |
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| / | \ |
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| / | \ |
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| / | \ |
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| / | \ |
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| / | \ |
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| / Lu | Ru \ |
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| /________|________\ |
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| / | / | \ | \ |
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| / | LBR / | \ RLB | \ |
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| B / | / | \ | \ B |
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| / | / | \ | \ |
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| / | / | \ | \ |
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| / LB | / LR | RL \ | RB \ |
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| / |/ | \| \ |
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| /________/________|________\________\ |
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| /| /| /|\ |\ |\ |
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| / | / | / | \ | \ | \ |
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| / | LDB / | LRD / | \ RDL | \ RBD | \ |
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| / | / | / | \ | \ | \ |
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| / | / | / | \ | \ | \ |
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| / | / | / | \ | \ | \ |
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| / Ll | / LD | / Lf | Rf \ | RD \ | Rr \ |
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| / |/ |/ | \| \| \ |
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| /________/________/________|________\________\________\ |
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| l D f D r |
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|Written by Jonathan Bowen |
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| Programming Research Group |
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| Oxford University Computing Laboratory |
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| 8-11 Keble Road |
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| Oxford OX1 3QD |
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| England |
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| Tel +44-865-273840 |
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|Created January 1982 |
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|Updated April 1985 |
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|Issue 1.1 |
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| Notation |
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|--------------------------------------------------------------|
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|1. Description |
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| ----------- |
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| The pyramix is a tetrahedral pyramid. Each face is |
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| divided into nine triangular segments. Any face and |
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| its adjacent segments on the other faces may be |
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| rotated relative to the rest of the pyramid. |
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| Alternatively the first two levels of segments from a |
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| vertex may be rotated relative to the opposite face. |
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| Additionally the extreme vertex segments may be |
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| rotated. |
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|2. Faces |
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| ----- |
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| The following uppercase letters are used to denote the |
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| four faces of the pyramid: |
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| B for the back face, |
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| L for the lefthand face, |
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| R for the righthand face, |
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| D for the downward face. |
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| The following lowercase letters are used to denote the |
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| four vertices of the pyramid: |
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| f for the front vertex, |
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| l for the lefthand vertex, |
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| r for the righthand vertex, |
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| u for the upward vertex. |
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| f l r u denote a clockwise rotation of the |
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| first two levels through 120 |
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| degrees about the indicated vertex. |
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| f- l- r- u- denote a similar rotation in an |
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| anticlockwise direction. |
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|3. Segments |
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| -------- |
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| Each segment of each face is represented by a string |
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| of one to three letters. The first letter indicates |
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| the face on which the segment is situated. The |
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| following letters indicate the adjacent face or faces |
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| (the order is not important). Note that the segments |
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| immediately adjacent to the vertices may be considered |
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| the same as the segments immediately adjacent on each |
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| face since the outer vertex segments may simply be |
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| rotated without affecting the rest of the pyramix. |
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| However these may be specified by the face (uppercase) |
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| followed by the vertex (lowercase) if desired. The |
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| The following are examples of segments: |
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| RD the segment on the righthand face in the |
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| centre of the edge next to the downward |
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| face. |
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| LBR or LRB the segment on the lefthand face at the |
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| touching the back and righthand faces. |
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| Bu the segment on the back face at the |
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| extreme upper vertex. |
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|4. Operation notation |
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| ------------------ |
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| Segments in brackets denote movement of the segments |
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| specified. Elements in the brackets are a cyclic group |
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| and rotate round one place from right to left when the |
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| operation is performed. E.g. (RL,LB,BR) is transformed |
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| to (LB,BR,RL). Note that the first element moves to |
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| the last position. |
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----------------------------------------------------------------
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| Operation |
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|--------------------------------------------------------------|
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|1. Rotate each of the extreme vertex segments until they |
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| match across to the adjacent segments. |
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|2. Make the vertex segments match on one face. First |
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| match two adjacent vertex segments. If the third |
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| vertex will not match, rotate the vertices round to |
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| to the adjacent face. The third vertex may now be |
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| rotated to match. |
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|3. Complete the face by rotating a vertex on the face, |
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| rotating the fourth vertex as necessary and then |
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| rotating the vertex on the face back again. The |
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| following moves are useful and will leave the lefthand |
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| face unaffected apart from one specified segment: |
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| (i) (LR,BR,...): f r- f- |
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| (ii) (LR,DR,...): u- r u |
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| (iii) (LR,RL) and ...: f r- f- r u- r u |
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|4. Now position completed face at the bottom and match |
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| the upper central portion to the bottom segments. |
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| Rotate the segments on the middle of the three upper |
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| edges using one of the following moves for a |
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| clockwise/anticlockwise rotation respectively: |
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| (iv) (RL,LB,BR): f u- f- u- f u- f- |
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| (v) (BR,LB,RL): f u f- u f u f- |
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|5. Flip the segments so that they are orientated |
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| properly using the following move: |
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| (vi) (RL,LR) and (RB,BR): f r- f- r u- r u r- |
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