'By the by,' he said, 'the Gryphon tells me that the sentencing for your fiction infraction is due in two weeks' time. Do you want to be present?'

This related to the time I had changed the ending to Jane Eyre. They found me guilty at my trial but the law's delay in the BookWorld just dragged things on and on.

'No,' I said after a pause. 'No, tell him to come and find me and let me know what my sentence will be.'

'I'll tell him. Well, toodle-oo,' said the Cat, and vanished, this time for good.

I pushed open the door of Mycroft's workshop with my toe, held it open for Pickwick to follow me in, then closed it before Alan could join us and placed the tray on a worktop. Mycroft and Polly were staring intently at a small and oddly shaped geometric solid made of brass.

'Thank you, pet,' said Polly. 'How are things with you?'

'Fair to not very good at all, Auntie.'

Polly was Mycroft's wife of some forty-two years and although seemingly in the background was actually almost as brilliant as her husband. She was a bouncy seventy and managed Mycroft's often irascible and forgetful nature with a patience that I found inspiring. 'The trick,' she told me once, 'is to regard him like a five-year-old with an IQ of two hundred and sixty.' She picked up her tea and blew on it.

'Still thinking about whether to put Smudger on defence?'

'I was thinking of Biffo, actually.'

'Smudger and Biffo would both be wasted on defence,' muttered Mycroft, making a fine adjustment on one face of the brass polyhedron with a file. 'You ought to put Snake on defence. He's untried, I admit, but he plays well and has youth on his side.'

'Well, I'm really leaving team strategy to Aubrey.'

'I hope he's up to it. What do you make of this?'

He handed me the solid and I turned the grapefruit-sized object over in my hands. Some of the faces were odd sided and some even sided — and some, strangely enough, appeared to be both. My eyes had trouble making sense of it.

'Very . . . pretty,' I replied. 'What does it do?'

'Do?' Mycroft smiled. 'Put it on the worktop and you'll see what it does!'

I placed it on the surface but the oddly shaped solid, unstable on the face I had placed it upon, tipped on to another. Then, after a moment's pause, it wobbled again and fell on to a third. It carried on in this jerky fashion across the worktop until it fell against a screwdriver, where it stopped.

'I call it a Nextahedron,' announced Mycroft, picking up the solid and placing it on the floor, where it continued its random perambulations, watched by Pickwick, who thought it might be chasing her, and ran away to hide. 'Most irregular solids are only unstable on one or two faces. The Nextahedron is unstable on all its faces - it will continue to fall and tip until a solid object impedes its progress.'