From @mail.uunet.ca:mark.longridge@canrem.com Mon Sep 4 23:11:05 1995 Return-Path: <@mail.uunet.ca:mark.longridge@canrem.com> Received: from seraph.uunet.ca (uunet.ca) by life.ai.mit.edu (4.1/AI-4.10) for /com/archive/cube-lovers id AA03764; Mon, 4 Sep 95 23:11:05 EDT Received: from portnoy.canrem.com ([198.133.42.17]) by mail.uunet.ca with SMTP id <210113-1>; Mon, 4 Sep 1995 23:13:08 -0400 Received: from canrem.com by portnoy.canrem.com (4.1/SMI-4.1) id AA07431; Mon, 4 Sep 95 23:06:36 EDT Received: by canrem.com (PCB-UUCP 1.1f) id 1F3009; Mon, 4 Sep 95 23:01:18 -0500 To: cube-lovers@life.ai.mit.edu Reply-To: CRSO.Cube@canrem.com Sender: CRSO.Cube@canrem.com Subject: Dino Cube From: mark.longridge@canrem.com (Mark Longridge) Message-Id: <60.1225.5834.0C1F3009@canrem.com> Date: Mon, 4 Sep 1995 23:41:00 -0400 Organization: CRS Online (Toronto, Ontario) # Here are a few Dino cube calculations. The calculations for the # cube with an X cut on each of the 6 sides, assuming period 3 # rotations of 3 edges (there are 8 of these, one for each corner) # The Dino cube has 12! /2 = 239,500,800 essential states # Fixing one edge gives the Dino cube a fixed orientation # in space and gives 11! /2 = 19,958,400 combinations # It has less combinations then the standard pyraminx, but more # than the 2x2x2 Rubik's Pocket cube. # The Dino cube has 12 edges which can not flip, observed by Rubik # himself back in 1982 (re: Rubik's Logic & Fantasy in Space.) # Dino cube has trivial centre dino := Group( (1,24,7) (2,23,5), (2,12,22) (4,11,24), (4,19,10) (3,17,12), (3,5,20) (1,6,19), (13,21,11) (14,22,9), (14,8,23) (16,7,21), (16,18,6) (15,20,8), (15,9,17) (13,10,18) );;