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Winter Olympics champion Lizzy Yarnold is backing an online campaign to get a post box in her hometown spray painted gold.
The Royal Mail decorated 47 post boxes in honour of gold medalists following London 2012.
But it has insisted this was a one off occasion because Britain hosted the Games.
It said it will instead look into other ways of honouring Yarnold, a former Maidstone Grammar School for Girls' pupil.
This could include creating a special postmark to recognise the achievements of top athletes.
But a Twitter campaign is hoping to force the organisation into a U-turn.
Fans of the athlete are using the hashtag #paintitgoldforlizzy to put the Royal Mail under pressure.
The 25-year-old, from West Kingsdown, has shown her appreciation by adding the hashtag to her Twitter profile.
She won Team GB's first gold medal at the Winter Olympics in Sochi on Friday in the women's skeleton after setting a track record.
Royal Mail spokesman Sally Hopkins said: "London 2012 was a unique occasion. The UK hosted the Games and our athletes performed extraordinarily well.
"Because of our status as the host nation we chose to mark the achievement of our athletes through gold post boxes as well as stamps.
"For the winter Olympics 2014 Royal Mail will not be creating gold postboxes but we are exploring other ways of marking the achievements of our athletes, including creating a special postmark."