User:Inthar/Ternary billiard words of length at most 31: Difference between revisions

The following are rotationally non-equivalent ternary [[billiard scales]] ax by cz of length at most 31, where a ≥ b ≥ c and gcd(a, b, c) = 1.  

= List =

== 1x1y1z ==

== 2x1y1z ==

== 2x2y1z ==

== 3x1y1z ==

== 3x2y1z ==

== 3x2y2z ==

== 3x3y1z ==

# xzyxzyxy

# zxyxzyxy

# zxyzxyxy

# xxxxzy

# xxxzxy

# xxzxxy

# xzxxxy

# zxxxxy

== 4x2y1z ==

# xxzyxxy

# xzxyxxy

# zxxyxxy

== 4x3y1z ==

== 4x3y2z ==

== 4x4y1z ==

# xzyxzyxzyxy

# zxyzxyxzyxy

# zxyzxyzxyxy

# xxxxxzy

# xxxxzxy

# xxxzxxy

#* maximum variety 3, balance 1

# xxzxxxy

#* maximum variety 3, balance 1

# xzxxxxy

# zxxxxxy

# xxxzyxxy

# xxzxyxxy

# xxzyxxxy

# xzxxyxxy

# xzxyxxxy

# zxxxyxxy

# zxxyxxxy

# xxzxyxzxy

# zxxxyzxxy

# xxxzyxxzy

# xxzxyxxzy

# xxzyxxyxy

# xxzyxyxxy

# xzxyxxyxy

# xzxyxyxxy

# xzyxxyxxy

# zxxyxxyxy

# zxxyxyxxy

# zxyxxyxxy

== 5x3y2z ==

== 5x4y1z ==

# xzxyxyxzyxy

# xzxyxyzxyxy

# xzyxxyzxyxy

# zxxyxyzxyxy

# zxyxxyzxyxy

# xxzyxyxzyxy

# xzyxxyxzyxy

# xzxyxzyxzyxy

# xzxyzxyxzyxy

# xzyxzxyxzyxy

# zxxyzxyxzyxy

# zxyxzxyxzyxy

# zxyxzyxxzyxy

# zxyxzxyzxyxy

# zxyxzyxzxyxy

# zxyxzyxzyxxy

# zxyzxyxzxyxy

# xzxyzxyzxyzxy

# zxxyzxyzxyzxy

# xzxyzxyxzyxzy

# xxzyxzyxzyxzy

== 5x5y1z ==

# xzyxyxzyxyxy

# zxyxyxzyxyxy

# zxyxyzxyxyxy

# zxyxzyxyzxyxy

# xzyxzyxzyxzyxy

# zxyzxyzxyxzyxy

# zxyzxyzxyzxyxy

# xxxxxxzy

# xxxxxzxy

# xxzxxxxy

# xzxxxxxy

# zxxxxxxy

# xxxzyxxxy

# xxzxyxxxy

# xzxxyxxxy

# zxxxyxxxy

# xxzyxxyxxy

# xzxyxxyxxy

#* maximum variety 4, balance 2

# zxxyxxyxxy

#* maximum variety 4, balance 2

== 6x3y2z ==

== 6x4y1z ==

# xzxyxzyxxzyxy

# zxxyzxyxzxyxy

# zxyxzxyxzyxxy

# xxzyxyxyxyxy

# xzxyxyxyxyxy

# xzyxxyxyxyxy

# xzyxyxxyxyxy

# xzyxyxyxxyxy

# xzyxyxyxyxxy

# zxxyxyxyxyxy

# zxyxxyxyxyxy

# zxyxyxxyxyxy

# zxyxyxyxxyxy

# zxyxyxyxyxxy

# xzxyxyxzyxyxy

# xzyxxyxzyxyxy

# xzyxyxxzyxyxy

# zxxyxyzxyxyxy

# zxyxxyzxyxyxy

# zxyxyxzxyxyxy

# zxyxyxzyxxyxy

# zxyxyxzyxyxxy

# xzxyxzyxyxzyxy

# xzyxxzyxyxzyxy

# zxxyzxyxyzxyxy

# zxyxzxyxyzxyxy

# zxyxzyxxyzxyxy

# zxyxzyxyxzxyxy

# zxyxzyxyxzyxxy

== 6x5y4z ==

# xzxyzxyxzyxzyxy

# xzyxzxyxzyxzyxy

# zxxyzxyzxyxzyxy

# zxyxzxyzxyxzyxy

# zxyxzyxzxyxzyxy

# zxyxzyxzyxxzyxy

# zxyzxyxzxyzxyxy

# zxyzxyxzyxzxyxy

# zxyzxyxzyxzyxxy

# xzxyzxyzxyzxyxzy

# xzxyzxyzxyzxyzxy

# zxxyzxyzxyzxyzxy

# xzxyzxyzxyxzyxzy

# xzxyzxyxzyxzyxzy

# xzxyxzyxzyxzyxzy

# xxzyxzyxzyxzyxzy

# xzyxyxyxyxyxy

# zxyxzyxzyxzyxzyxy

# zxyzxyxzyxzyxzyxy

# zxyzxyzxyzxyzxyxy

# xxxxxxxzy

# xxxxxxzxy

# xxxxxzxxy

# xxxxzxxxy

# xzxxxxxxy

# zxxxxxxxy

# xxxxzyxxxy

# xxxzxyxxxy

# xxxzyxxxxy

# xxzxxyxxxy

# xxzxyxxxxy

# xzxxxyxxxy

# xzxxyxxxxy

# zxxxxyxxxy

# zxxxyxxxxy

# xxzxxyxxzxy

# xzxxxyzxxxy

# zxxxxyzxxxy

# xxxxzyxxxzy

# xxxzxyxxxzy

# xxxzxyxxzxy

# xxxzyxxyxxy

# xxzxyxxyxxy

# xxzyxxxyxxy

# xxzyxxyxxxy

# xzxxyxxyxxy

# xzxyxxxyxxy

# xzxyxxyxxxy

# zxxxyxxyxxy

# zxxyxxxyxxy

# zxxyxxyxxxy

# xxzxyxxzyxxy

# xzxxyxxzyxxy

# xzxyxxxzyxxy

# xzxxyxzxyxxy

# xzxyxxzxyxxy

# xzxyxxzyxxxy

# zxxxyxzxyxxy

# zxxyxxzxyxxy

# zxxyxxzyxxxy

# zxxyxzxxyxxy

# zxxyxzxyxxxy

# xzxxyxzxyxzxy

# xzxxyzxxyzxxy

# zxxxyzxxyzxxy

# xxzxyxzxyxxzy

# xxzxyxzxyxzxy

# xxzxyxxzyxxzy

# xxzyxxyxxyxy

# xxzyxxyxyxxy

# xxzyxyxxyxxy

# xzxyxxyxxyxy

# xzxyxxyxyxxy

# xzxyxyxxyxxy

# xzyxxyxxyxxy

# zxxyxxyxxyxy

# zxxyxxyxyxxy

# zxxyxyxxyxxy

# zxyxxyxxyxxy

== 7x4y2z ==

# xzxyxxyxzxyxy

# xzxyxxyxzyxxy

# xzxyxxyzxxyxy

# xzxyxxyzxyxxy

# zxxyxxyzxxyxy

# zxxyxxyzxyxxy

# xxzyxxyxxzyxy

# xxzyxxyxzxyxy

# xxzyxxyxzyxxy

# xzxyxzxyxxzyxy

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# zxyxzxyxxzyxxy

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# zxyxzxyxzxyxxy

# xzxyxzxyzxxyzxy

# xzxyzxxyzxxyzxy

# zxxyzxxyzxxyzxy

# xzxyxzxyxzxyxzy

# xxzyxzxyxzxyxzy

# xxzyxxzyxxzyxzy

== 7x5y1z ==

# xzxyxyxxzyxyxy

# xzxyxyxzxyxyxy

# xzxyxyxzyxxyxy

# xzyxxyxzyxxyxy

# xzyxxyxzyxyxxy

# zxxyxyxzxyxyxy

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# zxxyzxyzxxyzxyzxy

# xzxyzxyxzxyzxyxzy

# xzxyxzyxzxyzxyxzy

# xxzyxzyxxzyxzyxzy

# xxzyxyxyxyxyxy

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# xzxyxzyxyxzyxzyxy

# xzyxxzyxyzxyxzyxy

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# zxxyzxyzxyxzyxzyxy

# zxyxzxyzxyxzyxzyxy

# zxyxzyxzxyxzyxzyxy

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# zxyzxyzxyxzyxzxyxy

# zxyzxyzxyxzyxzyxxy

# xzxyzxyzxyzxyzxyxzy

# xzxyzxyzxyzxyzxyzxy

# zxxyzxyzxyzxyzxyzxy

# xzxyzxyzxyzxyxzyxzy

# xzxyxzyxzyxzyxzyxzy

# xxzyxzyxzyxzyxzyxzy

# xzyxyxyxyxyxyxy

# zxyxyxyxzyxyxyxy

# xzyxyxzyxyxzyxyxy

# zxyxyxzyxyxzyxyxy

# xzyxzyxyxzyxyxzyxy

# zxyxzyxyxzyxyxzyxy

# zxyxzyxyxzyxyzxyxy

# zxyzxyxyzxyxyzxyxy

# xzyxzyxzyxyxzyxzyxy

# zxyxzyxzyxyxzyxzyxy

# zxyxzyxzyxyzxyxzyxy

# zxyzxyzxyxyzxyzxyxy

# xzyxzyxzyxzyxzyxzyxy