Tested on new install of Ubuntu 14.04

sudo apt-get install openjdk-7-jre
sudo apt-get install libjava3d-java
sudo cp /usr/share/java/j3d*.jar  /usr/lib/jvm/java-7-openjdk-amd64/jre/lib/ext/
sudo cp /usr/lib/jni/libj3dcore-ogl.so /usr/lib/jvm/java-7-openjdk-amd64/jre/lib/ext/
sudo cp /usr/share/java/vecmath-*.jar /usr/lib/jvm/java-7-openjdk-amd64/jre/lib/ext/
java -jar GenericPolytopes.jar 

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In order to install Java3D on an other operating system (like Windows) please follow the instructions on https://java3d.java.net/