--- a/README.md
+++ b/README.md
@@ -21,7 +21,7 @@
 using the command "polymake" at the Linux prompt. A few (optional) 
 functions rely on Singular software (available from 
 https://www.singular.uni-kl.de/) which should be installed so that it starts 
-using the command "singular" at the Linux prompt. A few (oprional) functions
+using the command "singular" at the Linux prompt. A few (optional) functions
 rely on Graphviz software (available from http://www.graphviz.org/).
 
 Please send your bug reports to graham.ellis(at)nuigalway.ie .
--- a/doc/newNewCellComplexes.xml
+++ b/doc/newNewCellComplexes.xml
@@ -163,9 +163,9 @@
 </Description> </ManSection> 
 <ManSection> <Func Name="Homology" Arg="C,n"/> <Func Name="Homology" Arg="F,n"/> <Func Name="Homology" Arg="K,n"/> <Func Name="Homology" Arg="K,n"/> <Func Name="Homology" Arg="K,n"/> <Func Name="Homology" Arg="K,n"/> <Func Name="Homology" Arg="K,n"/> <Description><P/> <P/> Inputs a chain complex <M>C</M> and integer <M>n \ge 0</M> and returns the <M>n</M>-th homology group of <M>C</M> as a list of its abelian invariants. <P/> Inputs a chain map <M>F</M> and integer <M>n \ge 0</M>. It returns the induced homology homomorphism <M>H_n(F)</M> as a homomorphism of finitely presented groups. <P/> Inputs a cubical, or pure cubical, or pure permutahedral or regular CW or simplicial complex <M>K</M> together with an integer <M>n \ge 0</M>. It returns the <M>n</M>-th integral homology group of <M>K</M> as a list of its abelian invariants. <P/><B>Examples:</B> <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap2.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap3.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap4.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap5.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap6.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap7.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap9.html</Link><LinkText>8</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap10.html</Link><LinkText>9</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap11.html</Link><LinkText>10</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap12.html</Link><LinkText>11</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap13.html</Link><LinkText>12</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap14.html</Link><LinkText>13</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLinks.html</Link><LinkText>14</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutArithmetic.html</Link><LinkText>15</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutMetrics.html</Link><LinkText>16</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutArtinGroups.html</Link><LinkText>17</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutAspherical.html</Link><LinkText>18</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutParallel.html</Link><LinkText>19</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutBredon.html</Link><LinkText>20</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPerformance.html</Link><LinkText>21</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCocycles.html</Link><LinkText>22</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>23</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPoincareSeries.html</Link><LinkText>24</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>25</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>26</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPolytopes.html</Link><LinkText>27</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoxeter.html</Link><LinkText>28</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutquasi.html</Link><LinkText>29</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCubical.html</Link><LinkText>30</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutRandomComplexes.html</Link><LinkText>31</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutRosenbergerMonster.html</Link><LinkText>32</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDavisComplex.html</Link><LinkText>33</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutDefinitions.html</Link><LinkText>34</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutSimplicialGroups.html</Link><LinkText>35</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutExtensions.html</Link><LinkText>36</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutSpaceGroup.html</Link><LinkText>37</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutFunctorial.html</Link><LinkText>38</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutGraphsOfGroups.html</Link><LinkText>39</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutIntro.html</Link><LinkText>40</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTensorSquare.html</Link><LinkText>41</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLieCovers.html</Link><LinkText>42</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTorAndExt.html</Link><LinkText>43</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLie.html</Link><LinkText>44</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTwistedCoefficients.html</Link><LinkText>45</LinkText></URL>&nbsp;
 </Description> </ManSection> </Section> <Section><Heading> Visualization</Heading> 
-<ManSection> <Func Name="BarCodeDisplay" Arg="L"/> <Description><P/> <P/>Displays a barcode <B>L=PersitentBettiNumbers(X,n)</B>. <P/><B>Examples:</B> <URL><Link>../tutorial/chap10.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>2</LinkText></URL>&nbsp;
+<ManSection> <Func Name="BarCodeDisplay" Arg="L"/> <Description><P/> <P/>Displays a barcode <B>L=PersistentBettiNumbers(X,n)</B>. <P/><B>Examples:</B> <URL><Link>../tutorial/chap10.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>2</LinkText></URL>&nbsp;
 </Description> </ManSection> 
-<ManSection> <Func Name="BarCodeCompactDisplay" Arg="L"/> <Description><P/> <P/>Displays a barcode <B>L=PersitentBettiNumbers(X,n)</B> in compact form. <P/><B>Examples:</B> <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap10.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>3</LinkText></URL>&nbsp;
+<ManSection> <Func Name="BarCodeCompactDisplay" Arg="L"/> <Description><P/> <P/>Displays a barcode <B>L=PersistentBettiNumbers(X,n)</B> in compact form. <P/><B>Examples:</B> <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap10.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>3</LinkText></URL>&nbsp;
 </Description> </ManSection> 
 <ManSection> <Func Name="CayleyGraphOfGroup" Arg="G,L"/> <Description><P/> <P/> Inputs a finite group <M>G</M> and a list <M>L</M> of elements in <M>G</M>.It displays the Cayley graph of the group generated by <M>L</M> where edge colours correspond to generators. <P/><B>Examples:</B> 
 </Description> </ManSection> 
